Plans to make wearing face masks on public transport compulsory in NI have been put on hold for the time being.
The executive briefly discussed the issue on Monday but decided to return to it later in the week.
Infrastructure Minister Nichola Mallon is keen to see face coverings introduced in line with Scotland and the Republic of Ireland.
However, First Minister Arlene Foster said the executive is looking for "clarity on legal advice".
"We're looking at legal advice in relation to if it becomes mandatory how we would do it in a way that is proportionate, that we don't criminalise people," Mrs Foster said.
"There are many people who may not be able to wear masks because of medical issues.
"So it's important that we do things in a proportionate way and that we don't rush into things just for the sake of it."
Also on Monday, Deputy First Minister Michelle O'Neill announced that limits to the number of people who could attend outdoor gatherings would increase to 30.
Further details on restrictions regarding funerals are expected to be discussed by the executive later this week.
Mrs O'Neill also said mourners attending the funeral of veteran republican Bobby Storey this week should observe social distancing.
The deputy first minister defended her decision to travel to Dublin at the weekend to attend a special meeting of the Dail.
She said it was "well within the regulations to travel" and said it was a "good decision to go".
On Monday, one more Covid-19 related death was reported in Northern Ireland, bringing the total of deaths in the pandemic recorded by the Department of Health to 551.
There have been six more confirmed cases of the virus, bringing that total to 5,757.
In the Republic of Ireland there were no further Covid-linked deaths and 24 additional cases in the last 24 hours.
Monday's moves come after Northern Ireland became the first part of the UK to make changes to the social distancing rule.
The rule in Northern Ireland has changed from two metres to one with certain conditions in place.
It was agreed by the executive last week, ahead of the hospitality sector preparing to reopen fully on Friday.
Face coverings on public transport became mandatory in the Republic of Ireland on Monday and has been in place in England and Scotland for weeks.
At present, the NI Executive strongly recommends face masks are worn in shops and on public transport, or if visiting people indoors, where it can be more difficult to maintain social distancing.
Ms Mallon, the infrastructure minister, has had discussions with unions and the police about the model of enforcement, which is likely to be similar to measures introduced in Scotland with spot checks by police and fines for those breaking the rules.
A number of other changes to Northern Ireland's lockdown took effect on Monday, including:
- Places of worship can reopen on a wider basis across NI for indoor services - with social distancing and cleaning of hard contact surfaces
- Elite athletes can train indoors and contact sport training can resume
- Childminders can care for the children of four families at one time
Last Thursday, the executive announced a series of additional indicative dates for the easing of the lockdown, with hairdressers able to reopen from 6 July.
The first minister attended a service at St Macartin's Cathedral in Enniskillen, County Fermanagh, on Monday.
She said it was "very important" that people continue "to observe social distancing and make sure that we keep people safe" but that it was also important "that people are able to come together and to witness".
"It has been incredibly difficult, particularly for those who have been mourning," she added.
The Very Reverend Kenneth Hall, who is Dean of Clogher and rector of the cathedral, said: "A lot of people do want to gather for worship, and today being St Peter's day, St Peter was the rock on which Christ built his church, and what better day to reopen."
Meanwhile, charity BirthWise is calling on Health Minister Robin Swann to update maternity guidelines.
It carried out a small survey last week which it said found that women were unhappy with the current arrangements.
Due to coronavirus, partners are unable to attend maternity scan appointments and partner visits are limited.
The Department of Health said that current restrictions on appointments and visiting are being reviewed and guidance would be published soon.