US presidential candidate Donald Trump says British Prime Minister David Cameron has asked him to visit London, but sources are questioning if that is the case.

The presumptive Republican White House nominee told MSNBC he received the invitation two days ago and he "might do it".

But sources suggest Mr Trump will only be invited to the UK by Mr Cameron once he becomes the official candidate and the same would go for whoever becomes the Democratic presidential nominee.

Mr Cameron's office said it was "long-standing practice" for Britain's prime minister to meet the Republican and Democratic presidential nominees, but emphasised that no firm meeting had been lined up.

Mr Trump's remarks follow criticism by Mr Cameron of the New York property baron's call for a temporary ban on Muslims entering the US.

In December, Mr Cameron called Mr Trump's proposal "divisive, stupid and wrong".

Mr Cameron stood by his earlier comments and refused to apologise when Mr Trump became the presumptive nominee this month as his two remaining rivals dropped out of the race.

The property magnate hit back on Monday, saying: "It looks like we're not going to have a very good relationship, who knows?".

The following day Mr Trump said he expected to have "a good relationship" with Mr Cameron.

On Friday, Mr Trump - who is set to formally clinch the nomination at July's Republican party convention - was talking of an invitation.

"I will do just fine with David Cameron," Mr Trump told MSNBC. "I think he's a nice guy. I will do just fine".

"But they have asked me to visit 10 Downing Street - and I might do it".

Mr Cameron has previously said he will work with the winner of November's US presidential election and is committed to maintaining the US-UK relationship, his spokesman has said.

The National Rifle Association, America's most powerful gun lobby, endorsed Mr Trump for president on Friday at its annual gathering in Louisville, Kentucky.