First Minister Mark Drakeford has come under pressure from his own Labour backbenchers over his ban on the sale of alcohol in Welsh pubs.
Alun Davies demanded to see evidence underlying the decision.
Meanwhile Hefin David said information from a group advising ministers should have been published when the decision was taken.
Mr Drakeford said the case for the need for the restrictions – aimed at easing a rise in cases – was “compelling”.
Pubs, bars and restaurants in Wales will not be able to serve alcohol on the premises from 18:00 GMT on Friday.
Welsh Conservative Senedd leader Paul Davies said many businesses will “not survive” the decision.
Plaid Cymru leader Adam Price said it was a “mistake”, said the changes were “not comprehensible” and could damage public trust.
Earlier the boss of Wales’ biggest brewery called the new alcohol rules “closure by stealth” and announced more than 100 managed pubs will be shut from Friday.
During a debate in the Welsh Parliament, Mr Drakeford told Senedd members: “If I have to make an unpopular decision because it is the right decision, I will make the right decision and not just the one that makes me popular.”
Wales is facing a “public health emergency”, he told members, and that the Welsh Government was relying on evidence used to close pubs in other parts of the UK.
Blaenau Gwent’s Mr Davies told the first minister that if he “wants myself and others to support him in these regulations, he must provide the evidence and advice has received from his advisers”.
He said that was needed so members could “explain those decisions to the people we represent”.
The Welsh Government has cited advice from UK government’s Scientific Advisory Group for Emergencies (Sage), as well as its own Technical Advisory Cell (TAC).
Mr Drakeford told Mr Davies that when he “has a chance to study what Sage has already said, what the TAC will tell him what the figures of positivity, transmission, hospitalisation and death in his part of Wales tell him, he will see very plainly why the actions we are taking are necessary and necessary now”.
Mr David was more supportive of the first minister, saying there was “a logic behind what the government has done”, based on advice from Sage.
However he added: “There is a lot of frustration and anger out there with regard to this decision.”
The Welsh Government’s Technical Advisory Cell usually publishes its latest Covid-19 advice on Thursdays.
“It should be when the decision is announced,” Mr David said.
Mr Drakeford said “we will do our best to expedite” TAC advice but he said they “provide it when they are confident that they’ve got it ready for publication, and it’s very important that I do not attempt to try to influence them in the work that they do”.
Over the course of the day in the Senedd, Mr Drakeford faced calls from the opposition for the scientific basis of the decision to be published.
Mr Drakeford said the evidence is there “in the public health emergency we are facing”.
“Two of our local authorities in Wales have rates of more than 400 per 100,000 of the population; seven of them rates of over 300; 11 of them rates over 200, and those rates are growing – growing across Wales.
“The evidence for the actions we are taking is there to be seen in the reviews published by Sage on 11 and 19 November, reviewing the measures that have succeeded across the United Kingdom, and we have drawn on that to put in place in Wales those steps that will reduce the flow of coronavirus and save lives that need not be lost.
“It’s the same evidence that [the UK government] has drawn on to close pubs and prevent the sale of alcohol in tier 3 levels in England; it’s the same evidence that led the SNP Government in Scotland to close pubs and to prevent the sale of alcohol in level 3 areas in Scotland. It’s why hospitality is closed in Northern Ireland today.”
Pubs are closed in tier 3 areas in England, while in level 3 areas in Scotland they are not able to serve alcohol.
During First Minister’s Questions, Paul Davies described the decision as “catastrophic” and “devastating” for businesses.
“Pubs and restaurants in areas where transmission rates are low will rightly feel upset that their businesses is being put at risk, through no fault of their own,” he added.
Adam Price has called for ministers to allow alcohol to be served until 1900, with a ban on off-licence sales after that time, in what he said would be a “sensible compromise”.
“Off licences and supermarkets should not be allowed to sell alcohol after this time to discourage people from going into each other’s homes,” he said.