Republican presidential candidate Donald Trump has confirmed he would consider former rival Ted Cruz — who he repeatedly called "Lyin' Ted" during the party's brutal selection battle — as his vice-presidential candidate.

Mr Trump is the last man standing in the Republican race after his only remaining rivals, Mr Cruz and John Kasich, put their campaigns on hold.

In an interview with Bill O'Reilly on Fox News, real estate mogul Mr Trump was asked firstly if he would consider Mr Cruz in his administration.

"He's certainly a capable guy, so it's something we can think about," he said.

Mr Kasich was also suggested by O'Reilly as "a good VP".

"I would certainly consider him, he's someone I've gotten along with, during the debates during intermission I would always seem to be talking to John," Mr Trump said.

O'Reilly then asked if Mr Rubio could also be on the radar for an administrative role, saying Mr Trump needed to win Mr Rubio's home state of Florida.

"I am considering a number of people ... I would certainly consider him," Mr Trump said.

Mr Trump's immediate challenge is to unite deep fissures within the Republican Party, easing tensions with party loyalists who are appalled at his bullying style, his treatment of women and his proposals to build a wall on the border with Mexico and deport 11 million illegal immigrants.

This week he caused a furore by linking Mr Cruz's father to the 1963 assassination of John F Kennedy, citing a supermarket tabloid story which claimed Rafael Cruz, an immigrant from Cuba, was "with Lee Harvey Oswald" before the assassination.

Senator Cruz responded sarcastically at a campaign event in Indiana, branding Mr Trump a "pathological liar" and "amoral".

"And while I'm at it I guess I should go ahead and admit yes, my dad killed JFK, he is secretly Elvis, and Jimmy Hoffa is buried in his backyard," he said.

"This is just kooky. The man is utterly a moron."

A New York Times editorial published after Mr Cruz withdrew from the race quoted US election analyst Henry Olsen, commenting on the situation the Republican Party now found itself in, as saying that "I'm watching a 160-year-old political party commit suicide."