Liam Fox has told Brexiter MPs to put their “ideological purity” aside and support the government in Thursday’s vote on Brexit.

Members of the hard Brexit European Research Group are threatening to inflict another House of Commons defeat on the prime minister over the wording of a Downing Street amendment. They fear it it endorses the non-binding Spelman amendment backed by MPs, which rejected leaving the EU without a deal.

Fox, a strong leave supporter, urged the ERG to compromise on Thursday or risk undermining Theresa May’s negotiations with European leaders.

“There is a danger that we send the wrong signals,” the international trade secretary told BBC Radio 4’s Today programme.

Asked what his message was to Tory MPs intent on voting against the government, Fox said: “There is a tendency still to think that this is some kind of academic and ideological purity exercise. This is about the raw politics of negotiation and this is about sending signals back about continuity and trustworthiness in negotiation.

“It is important to understand that we are not an internal debating society in parliament. What we say is looked at and listened to by those that we are negotiating with. They’ll be looking to see whether parliament is showing consistency.

“Parliament said we don’t want there to be no deal and that we will sign up to the prime minister’s deal if we are able to get changes to the Irish backstop.

“Our European partners will be watching our debate and listening today to see if they get the impression that if they were to make those concessions, parliament would definitely deliver on that agreement.”

Fox said MPs had a “duty” to back the prime minister because her withdrawal deal represented the will of the public.

“We need to understand that the public wants us to leave the European Union, but they would prefer us to leave the European Union with a deal. And therefore parliament has got a duty to ensure that we send the correct signals that represent those views of the British people and represent them to those we are negotiating with,” he said.

“What is happening today is about whether we can display to our European partners that the prime minister has the support of the house in continuing to negotiate changes to the Irish backstop.

“And I think there is a willingness on the part of our European partners to accommodate us, but they will be wanting to see that Britain will be able to deliver if they were willing to compromise on that.”

Fox downplayed his department’s failure to roll over EU trade deals with other countries in time for the 29 March Brexit deadline.

“Of the 11% of our trade that is covered by the EU free-trade agreements, 20 of those 40 [countries] make up less than point eight of 1% of all our trade.”

And he pointed out the best way to ensure trade continued was to back the withdrawal agreement.

“We will get continuity of all of them if we get a deal and a withdrawal agreement agreed with the European Union. There is always a chance that we don’t get them, we are in fact well in advance with some of those biggest ones,” he said.