People in Wales will be able to travel to a small list of countries from Monday without going into quarantine when they get back.
But despite adopting the traffic-light system used in England, ministers are advising people not to go abroad.
The first minister warned it was "best avoided" because of concerns travellers could bring Covid with them.
Meanwhile, he revealed he had planned to go further in easing Covid rules but paused because of the Indian variant.
Plans to allow pubs to trade indoors, and for cinemas and museums to reopen, will go ahead from Monday.
Ministers had considered relaxing lockdown restrictions further on the same, but Mark Drakeford said officials had "decided to hold back" for more advice.
He told the BBC he had been considering allowing "some small events" and "greater mixing between people not in a household".
Both are now on hold.
Eleven cases 'of concern'
Experts are concerned the variant has mutations that may make it more transmissible, but it is not yet known if it causes more severe disease or if it might make current vaccines less effective.
A total of 26 cases of two variants first identified in India had been found in Wales as of last Thursday - including 11 of a type identified by officials as a "variant of concern".
A total of 1,313 cases of the variant of concern have been identified in the UK.
No change to Welsh vaccine programme
Prime Minister Boris Johnson announced on Friday evening the wait between jabs will be cut from 12 weeks to eight for the over-50s and clinically vulnerable because of concern over the Indian variant.
The change does not apply in Wales and the Welsh government said it will continue with the rollout as planned.
A Welsh government spokesperson said: "We have considered the latest evidence and advice from the [Joint Committee on Vaccination and Immunisation].
"Given the low numbers of the Indian variant and the high numbers of people in Wales already vaccinated, we are confident that our vaccination programme already has the flexibility it needs to respond swiftly and effectively and are not making any changes at this stage."
New rules on international travel
People in England and Scotland can take holidays abroad in a small number of so-called "green" countries - including Portugal, Israel and Singapore - without having to quarantine when they return.
Wales will be adopting the same "traffic light" system, with countries classified as green, amber and red.
It means people will be able to travel to a small number of foreign destinations in the green list without the need to quarantine on their return.
Mandatory quarantine for countries not on the green list remains in place, and visitors to red list countries will need to book hotels on their return.
Everyone who travels will need to book at least one test on their return.
However, the Welsh government said it would continue to advise people to only travel for essential purposes.
Mr Drakeford said: "This is the year to take your holiday in Wales and foreign travel is best avoided."
He admitted his travel advice was not a rule because it would be "unenforceable". He urged caution against "importing" coronavirus from other parts of the world.
"We know most people who travel from Wales will be doing it from Bristol, Manchester, London, so once those airports are open and travel across the UK is allowed, then people from Wales will be able to travel," he said.
Mr Drakeford told a press conference on Friday he did not want to "make people feel guilty" about going abroad, but urged people to "think of their own safety and the safety of others", adding there were "fantastic opportunities" to take a holiday in Wales instead.
Will there be a vaccine passport?
From 24 May, a "paper-based vaccination status" will be available for people in Wales who have had two doses of vaccination and need to urgently travel to a country that requires Covid vaccination proof.
A UK government app that will act as a vaccine passport is due to be available in England on Monday, but the first minister said there was likely to be a four-week gap before it could be used in Wales due to technical reasons.
What Covid rules are changing on Monday?
Mr Drakeford told the press conference Wales would move to Covid alert level two from Monday, meaning:
- Pubs and restaurants can reopen indoors for groups of six people from up to six different households
- Holiday accommodation can fully reopen
- Cinemas, theatres bingo halls, bowling alleys, indoor play centres and areas, casinos and amusement arcade can reopen
- Up to 30 people can take part in indoor activities, and up to 50 in organised outdoor activities
From 24 May, restrictions on numbers of visitors to care homes will be eased.
Mr Drakeford said that, if the situation remained positive at the start of June, he would look at whether Wales could move to alert level one.
But he warned he may need to delay that because of the Indian variant.
This move would include "looking at relaxing the rules further around people meeting in their own homes, increasing the number of people able to attend wedding receptions and restarting larger events".
How have businesses reacted?
Ellen Morris, the owner of two pubs in Bala, Gwynedd, welcomed the relaxation of the rules but said it would be difficult to police rules which dictate only six people from six different household can meet.
"They are grown adults - they should be able to decide, it shouldn't be me telling them you can do this," she told BBC Radio Wales.
"They call it hospitality - I don't feel I'm being very hospitable these days. We are talking about people's mental health here. It's been a long enough year without being left out of groups."
Mr Drakeford said social distancing rules in hospitality venues could be lifted if transmissions continued to fall.
DJ Stacey Alford, from Penarth, Vale of Glamorgan, has been receiving support from the UK government's freelancers' fund and Universal Credit.
She said she had been "extremely cautious" and followed the rules very closely, but was frustrated by stricter rules in Wales than in England.
"My bugbear is we can't even do things like background noise, so those opportunities are gone, but DJs in England are able to do that."
The relaxation will also mean indoor play centres can open, and indoor wedding ceremonies of up to 30 people can take place.
Gail Windley, a wedding planner from Swansea, welcomed the news but said it would still mean weddings would be too small for most couples, and criticised a lack of clarity about further easing.
Charmaine Heydenrych, who owns a soft play centre in Cardiff, said she was "ready" to open but said being limited to 30 people was "not sustainable".
What have opposition politicians said?
Welsh Conservative Russell George welcomed the move to level two but said the Welsh government "should have outlined a roadmap to give hope to businesses and communities".
"It is concerning that the Welsh Government has indicated that social distancing and mask wearing will be required into the Autumn.
"What people really want is for the Welsh and UK governments to work together, to end the confusion over different restrictions in the two countries, especially as the virus does not recognise borders."
Plaid Cymru leader Adam Price welcomed the first minister's call for people to holiday in Wales rather than go aboard.
"It's a positive message - we need it for the economy as well. It's not just about greater health protection but also supporting tourism and hospitality businesses which have had a torrid time".
Mr Price said the sector still needed further financial support: "What is the plan for the months ahead for hospitality?".
Is the Indian variant in Wales because of travel?
The 26 cases of two variants first fouind in India are "almost entirely the result of international travel", the first minister said.
Mr Drakeford said those infected were "people coming back to Wales from overseas" and all cases were being carefully monitored by local public health teams.
"All the information I have had is that the individuals involved are following all the advice that they are required to follow, self-isolating and so on," he said.
"And the advice I have is not that we need to be overly concerned about the position in Wales at the moment."
Dr Gill Richardson, deputy chief medical officer for vaccines in Wales, told BBC Wales "we're not led to believe that it will evade the vaccine at this point".
Public Health Wales told BBC Wales it was not identifying where the 11 variant of concern cases were "due to the risk of small number identification".
Dr Robin Howe, incident director for Public Health Wales, said the majority of cases were associated with travel or with known contact, with the remainder still under investigation.