London (AFP) - An MP from British Prime Minister Theresa May's Conservative Party on Saturday revealed he would be barred from entering the US under President Donald Trump's immigration clampdown, presenting his boss with a diplomatic headache.

Iraqi-born MP Nadhim Zahawi tweeted that he had had "confirmation that the order does apply to myself and my wife as we were both born in Iraq," even though the pair have British passports.

"A sad sad day to feel like a second class citizen! Sad day for the USA," he added.

The revelation presents May with a diplomatic quandary having become the first international leader to meet the US president on Friday, where the pair discussed the possibility of a swift trade deal after Britain leaves the European Union.

Following his meeting with May, Trump on Friday signed a sweeping executive order to suspend the arrival of refugees and impose tough new controls on travellers from Iran, Iraq, Libya, Somalia, Syria and Yemen.

May refused to condemn the order despite being repeatedly pressed at a news conference during a trip to Turkey, saying Washington was responsible for its own refugee policy.

"The United States is responsible for the United States' policy on refugees," she said. "The United Kingdom is responsible for the United Kingdom's policy on refugees."

However, the involvement of British citizens has ramped up the pressure from members of her own party to condemn the president's stance, threatening the goodwill built up during her visit to Washington.

Tory MP Sarah Wollaston called Trump "a sickening piece of work" and demanded that he not be allowed to address both of Britain's Houses of Parliament when he makes a state visit late in the year, when he will be hosted by Queen Elizabeth II.

Opposition Labour MP Yvette Cooper said that May's refusal to condemn Trump "shames Britain".