British Prime Minister Theresa May on Monday refused to back down on inviting US President Donald Trump for a glitzy state visit, despite a petition gaining more than 1.5 million signatures and protesters rallying across the country.

May is standing firm on the invitation, which would see Trump honoured by parliament and Queen Elizabeth II, despite the premier's office saying she does not agree with his controversial ban on refugees and citizens of seven mainly Muslim countries.

"The United States is a close ally of the UK, we work together across many areas of mutual interest and we have that special relationship between us," May told a press conference in Dublin alongside her Irish counterpart Enda Kenny.

"I have issued that invitation for a state visit to President Trump to the UK and that invitation stands."

The British premier added: "In relation to the policies that have been announced by the US, the UK takes a different approach."

May announced the state visit during a meeting with Trump at the White House on Friday, which was intended to boost trade ties after Britain leaves the European Union.

But her closeness to the US leader drew fire at home, particularly when she initially failed to condemn the travel ban, saying it was a US affair.

Opposition Labour leader Jeremy Corbyn, the smaller Liberal Democrats and the Scottish National Party have all called for the state visit to be cancelled, as have some from May's own party.