The first minister has been accused of acting like a dictator after saying a senior Welsh Tory called for lockdown laws to be broken.
In a letter, Mark Drakeford objected to a tweet from Andrew RT Davies saying major food retailers should "take a stand" for their customers.
The Conservatives' health spokesman opposes rules banning the sale of non-essential items in supermarkets.
Mr Davies said the letter was "pathetic".
It is the second time the first minister has accused Conservatives of encouraging people to break coronavirus rules.
Ahead of a meeting between supermarkets and the Welsh Government, Mr Davies tweeted on Monday: "In the absence of any commons sense emerging at the top of government, please do take a stand for your customers. Wales is behind you."
Mr Drakeford responded in a letter to Mr Davies's boss, Paul Davies.
He told the Welsh Conservative Senedd leader: "While your group has made it clear you do not support this two-week firebreak to bring coronavirus under control and to save lives, it is another thing for the Welsh Conservatives' health spokesperson - an elected Member of the Senedd and a lawmaker - to be advocating people and companies break the law.
"We need everyone to work together to make this firebreak successful if we are to prevent the NHS from being overwhelmed and even more people losing their lives this winter."
He asked for confirmation that "from now onwards, the whole of the Welsh Conservatives group in the Senedd will be unambiguous in its support for the law".
In response, Andrew RT Davies said "we're all entitled to an opinion".
"For Labour's first minister to go into work this morning and set out to intimidate members of the Senedd is a disgrace and there should be no room in Welsh democracy for these dictator-style tactics," he added.
"I'm astonished that during a pandemic with deaths rising and the Welsh economy crashing, Mark Drakeford has time on his hands to compose such pathetic and inaccurate letters."
In a decision announced on Tuesday, Welsh Government listed baby clothes as essential items during the firebreak lockdown.
It also said customers should be able to ask for non-essential items in exceptional circumstances.
Earlier in October, Mr Drakeford objected to comments from north Wales Conservatives that earlier local lockdowns in the region were disproportionate.