International Trade Secretary Liam Fox has insisted the Cabinet has not agreed a deal to allow free movement of labour for three years after Brexit.
Dr Fox said that any such move would "not keep faith" with the referendum result.
He told The Sunday Times: "If there have been discussions on that I have not been party to them. I have not been involved in any discussions on that."
The intervention comes after Chancellor Philip Hammond said there was "broad acceptance" in Cabinet of a post-Brexit transitional period lasting up to three years.
He said this would mean "many arrangements remaining very similar to how they were the day before we exited the European Union".
Mr Hammond said there would be a registration system in place for people coming to work in the UK after Brexit, during the transitional period.
"If they come here to work after we leave the European Union, during that transitional period, the sensible approach will be to seek to register people so that we know who's coming and who's going," he said.
Tory tensions were also on show as former Brexit minister David Jones branded Mr Hammond's transition initiative "deeply dangerous" as he accused the Chancellor of "going on manoeuvres" while Prime Minister Theresa May was abroad on holiday.
"All this agitation by the Chancellor and his allies is hugely discourteous to her and undermines her authority," Mr Jones said in The Mail on Sunday.
Pro-EU Tory MP Sir Nicholas Soames praised the Chancellor, telling the newspaper: "He has restored discipline to the political infant class who want Brexit at any cost.
"Instead of mindlessly criticising him, they should thank him for putting a stop to what was in danger of becoming a pub brawl."
The war of words came as an ally of Foreign Secretary Boris Johnson also criticised Mr Hammond's plans.
Gerard Lyons, who was an economic adviser to Mr Johnson when he was London mayor, said a two-year transition period would work better.
Writing in The Sunday Telegraph, he said: "Many of the 'risks' being highlighted about Brexit are perceived risks, not real risks. And a two-year transition would alleviate many concerns."
Mr Johnson has not yet commented publicly on Mr Hammond's transition plans.
Meanwhile, divisions in Labour over Brexit emerged as senior figures urged Jeremy Corbyn to commit to staying in the single market.
The Observer reported that opponents of quitting the single market may provoke a showdown at the party's autumn conference by trying to force a vote on the issue.
Former leader Lord Kinnock told the newspaper: "The only way to mitigate the dreadful instability that will be costly for communities and industry is to try to ensure that, at least for a transitional period, we retain participation in the single market or the customs union, or both."
Ex-lord chancellor Lord Falconer also backed staying in the single market and TUC general secretary Frances O'Grady insisted the UK should not quit.
Writing in The Mail on Sunday, she said: "If there's another way of getting a frictionless trade deal that protects jobs and rights at work, trade unions would love to know."
Mr Corbyn has said that Britain would leave the single market on Brexit, while other leading party figures like shadow chancellor John McDonnell have said all options are on the table.