First Minister Mark Drakeford has threatened a travel ban in Wales on people from English Covid hotspots if the prime minister does not impose his own.
He said he is giving UK ministers "one final opportunity" before he makes changes in Welsh law.
The UK government announced on Monday that it will advise against non-essential travel from Merseyside.
But it stopped short of making it illegal, angering Welsh ministers.
Mr Drakeford said he could close the border with England, but that is not his preferred option.
Welsh ministers have asked for travel from areas with high rates of coronavirus in England to be restricted, to prevent people visiting parts of Wales where lockdowns are not in force and where rates are lower.
In 17 Welsh areas under local lockdown, people are subject to travel restrictions and cannot go in or out of the areas concerned except for a limited set of reasons, including to go to work or school.
They are not allowed to leave to go on holiday.
The Liverpool City Region will be placed on the "very high risk" Covid alert level from Wednesday, and Prime Minister Boris Johnson has warned people in the area not to go on holiday to Wales.
However, UK government ministers who govern Covid rules in England have not made it illegal to travel.
Speaking on BBC Wales Today, Mr Drakeford said he would be writing a letter to the prime minister spelling out the powers he has.
"If he doesn't act, we will use them," he said.
"I want to offer him one final opportunity to do the right thing, because that would be fair to people in Wales, and people across our border.
"I don't want it to be a border issue. People in England in high incidence areas should not be going to low incidence areas in England, either."
He said the prime minister's solution of guidance "simply will not do", saying North Wales Police cannot turn people away on the basis of it.
"We need rules that prevent people from high incidence areas coming into Wales to low incidence areas," he said.
He said the letter will provide evidence, requested by UK government ministers, that people moving from areas with high levels of the virus to areas with low levels spread the virus.
A Welsh Government spokesman said they want to receive a reply "within days".
It is the second time the first minister has written to the PM asking for a travel ban.
After the first time, the Mr Johnson rejected the proposal in an interview with BBC Wales.
"I don't want to impose travel restrictions within the UK generally," he said at the time.
'Is it fair?'
It came after a coach of holidaymakers from Bolton travelled to Pembrokeshire after a lockdown was imposed in Bridgend, where they were originally due to go for an Elvis festival.
In the Commons on Monday Plaid Cymru MP Liz Saville Roberts asked if it is fair that people in Liverpool can holiday in Gwynedd and Anglesey, when people in neighbouring Conwy cannot make non-essential journeys outside of the county.
Mr Johnson replied: "The guidance is very clear that people from very high areas such as Merseyside should not be making those journeys."
Mr Drakeford and Health Minister Vaughan Gething spoke to the prime minister on Monday morning in a Cobra meeting.
Afterwards the Welsh Government said Mr Drakeford had "expressed deep disappointment at the inadequate proposals for travel restrictions in high infection areas in England".
At a press conference Mr Gething outlined how travel restrictions between Wales and English Covid hotspots could work.
"We should, if needed, be able to identify those areas where the risk is such that we should have restrictions on travel," he said.
"It would not be a reasonable excuse for those people to enter Wales because of the risk that they present because of the area of the country that they come from."
The prime minister has already refused to introduce a travel ban in English Covid hotspots.
So why is the first minister asking again, rather than simply using the powers the Welsh Government has?
It probably reflects ideological as well as practical difficulties.
Welsh Labour is a pro-union party and the idea of legislation banning some people from England crossing the Welsh border might sit uncomfortably.
Remember that, during the national lockdown, the Welsh "stay local" rule applied across Wales - it didn't single out any particular group of people.
The practical problems include messaging and enforceability - the border sees millions of crossings every week and filtering lawful from unlawful journeys could be a major headache.