Michael Gove has opposed the suggestion by the trade secretary, Liam Fox, that the UK should be open to the prospect of allowing poultry treated with a chlorine wash process, which is banned by the EU, as part of a trade deal with the US.

The row has overshadowed Mr Fox’s trip to America this week to discuss the potential for a deal and, on Wednesday, Mr Gove went further, indicating that lowering environmental or agricultural standards would be a deal-breaker.

On BBC Radio 4’s Today programme, he was asked whether chlorinated chicken, given as an example of a product that does not meet EU standards but which the US produces, should be allowed. "No," he said.

Mr Gove agreed that the US would have give a to "kiss goodbye" to a trade deal if it included such imports. "Critically, we need to ensure that we do not compromise those standards. And I said last week when I was speaking to the WWF environmental charity that we need to be in a position as we leave the European Union to be leaders in environmental and in animal welfare standards."

Theresa May’s spokesman did not respond to a request for comment on Wednesday and has repeatedly declined to answer questions about food standards protections during trade negotiations in the past.

Mr Gove has said that maintaining safety and public confidence in food is of the highest priority, but that it is too early to get into the specifics and "hypotheticals" of any deal. "Any future trade deal must work for UK farmers, businesses and consumers," he added.

Mr Fox has faced tough questioning on the issue but has insisted it is a minor detail in complex potential negotiations. He dismissed a question about whether he would eat a chlorine-washed chicken himself, saying the media were obsessed with the topic, which was a "detail of the very end-stage of one sector of a potential free trade agreement."

A source close to the trade secretary was quoted by the Telegraph as saying he believed that "Americans have been eating it perfectly safely for years" and that any meaningful trade deal with the US would have to include agriculture.

Despite the clear cabinet split, Mr Gove insisted the government was united on the need not to "dilute our high animal welfare standards or our high environmental standards in pursuit of any trade deal."

He said: "The trade secretary quite rightly pointed out that, of course, this issue is important. But we mustn’t concentrate on this one issue when we look at the huge potential that a trade deal can bring."

Mr Fox has been criticised by Gianni Pittella, the leader of the socialist group in the European parliament, for his "indigestible" suggestion, which he said would lead the EU towards introducing controls on goods imported from the UK. "We won’t accept a race to the bottom on standards," he said.

Speaking on the BBC’s Newsnight programme on Tuesday, Mr Fox claimed the UK could accept products such as chlorinated chicken and protect its standards because there was no direct health risk.

The EU bans the practice because it says abattoirs could come to rely on it as a decontaminant and unscrupulous producers could use it to make meat appear fresher.

Moves to lift the ban are likely to be opposed by British farmers because American chicken is significantly cheaper than the UK’s produce. Barry Gardiner, the shadow trade secretary, said Mr Fox’s comments showed you should "never trust a Fox in your hen coop".

Brussels attacks Liam Fox's 'ignorant' remarks on chlorinated chicken

He added: "By arguing the case for chlorine-washed chicken, Liam Fox shows he is ready to abandon British poultry farmers in favour of cheap US imports that do not meet our sanitary or animal welfare standards.

"The US is our biggest trading partner outside of the EU and accounts for 17 per cent of British exports. We want to see that figure grow and every effort must be made to support British exporters and reduce unnecessary barriers to trade, but never at the expense of the interests of British consumers and producers."