David Cameron is to host Mitt Romney in Downing Street on Thursday in a meeting that will require delicate diplomatic handling by the prime minister.

The Republican nominee for the US presidential election will be stopping off in London for the opening ceremony of the Olympics at the start of a tour that will also take him to Poland and Israel.

The Romney camp expressed unease after the prime minister was given the full red carpet treatment at the White House by Barack Obama and a trip on Air Force One to the swing state of Ohio in March. Republicans were upset that the leader of their main sister party in Europe accepted such a high profile invitation from a Democratic president at a sensitive time in the electoral cycle.

Downing Street has struggled to explain in recent weeks why the prime minister has agreed to meet the Republican nominee in No 10 after refusing to meet François Hollande while he enjoyed the same status – a presidential candidate from a country that is a close ally. No 10 said at the time of the Hollande visit that the prime minister did not meet candidates in elections.

Asked whether No 10 had now changed its position on meeting election candidates, his spokesman said: "We have been through this so you know the position. The rules are as they were. They are the same and we are applying them."

Downing Street declined to say whether Cameron would greet Romney with a handshake in public on the No 10 doorstep. "We will come back to you on details of that," the spokesman said when asked whether they would meet publicly.

Cameron's team criticised Gordon Brown in 2008 when the then prime minister declined to greet Barack Obama on the No 10 doorstep because he was the Democratic nominee and not president. In a compromise Brown agreed to be photographed talking to Obama in the No 10 garden.

Cameron tried to upstage Brown by walking with Obama from the No 10 gates to parliament. This was rejected by the Obama team out of sensitivity to Brown.

Asked whether Cameron would follow the precedent set by Brown, the No 10 spokesman said: "We will come back to you on all of these things. We have been through these 100 times in recent weeks."