ROME, N.Y. - Texas Sen. Ted Cruz blasted rival Donald Trump in a radio interview Tuesday, accusing the Republican front-runner of being a bully, inciting violence and using dirty tricks to intimidate voters and delegates, as Trump continued to rail against a nominating system he says is crooked and rigged.

Using some of the harshest rhetoric of the campaign to date, Cruz said his billionaire rival is a bad businessman who has been surrounded by sycophants his entire career.

"Donald's whole pitch is he's a great businessman," Cruz said in a wide-ranging interview on the Glenn Beck radio show, adding that given how Trump runs his campaign, "it appears he can't run a lemonade stand."

The comments came as both campaigns work tirelessly behind the scenes to secure delegates who will back them at the Republican Party convention this summer in Cleveland. So far, Trump has appeared badly outmanoeuvred by a better-organized Cruz operation, prompting the real estate mogul to rail against the Republican electoral system, claiming that the will of the voters is being denied.

"Our Republican system is absolutely rigged. It's a phoney deal," said Trump at a rally in a packed airport hangar in Rome, New York, on Tuesday evening, where his speech was dominated by foot-stomping over the primary process.

He pointed to Colorado, where he said the delegate-selection system was set up by "crooked politicians" to make sure an outsider like him could never win.

"These are dirty tricksters," he said, placing the blame on the Republican National Committee. "They should be ashamed of themselves for allowing this kind of crap to happen," he added, saying that both Republicans and Democrats have set up "phoney rules and regulations" that makes it "impossible for a guy that wins to win."

He went further a few hours later during a CNN town hall in New York City, suggesting the RNC was actively working to defeat him.

"The RNC doesn't like this happening. They don't like that I'm putting up my own money because it means they don't have any control over me," Trump said, arguing that the deck is "stacked against me by the establishment."

On Monday, RNC Chairman Reince Priebus responded to Trump's complaints, declaring that "the rules are the rules."

Trump has built a 200-delegate lead over Cruz based on primary and caucus results, and is the only candidate with a realistic chance to secure the 1,237 delegates needed to win the nomination outright on the first ballot. Cruz's best hope for the nomination is for a contested convention in which pledged delegates become free to vote for any candidate after the first ballot. That's why his campaign is trying to have its own supporters selected as delegates even if they must vote for Trump on the first ballot.

Cruz, in the radio interview, unloaded on Trump over reports that his supporters were publishing the home addresses of delegates in Colorado and threatening to make public the hotel room numbers of delegates at the convention this summer.

"That is the tactic of union thugs," Cruz said. "That is violence. It is oppressive. The idea that Donald is threatening delegates, we're seeing that pattern over and over again."

Cruz even compared Trump to the lead character from "The Godfather."

"Donald needs to understand he's not Michael Corleone," Cruz said. "Donald needs to stop threatening the voters. He needs to stop threatening the delegates. He is not a mobster."

Cruz also discounted the seriousness of the Trump candidacy, saying: "There was a real chance this was a lark, this was 'let's get some publicity, let's have some fun.' And I think he was surprised as anybody."

Cruz joked that Trump is doing so poorly in securing delegates that if he were on his own reality TV show, "The Apprentice," he would have to fire himself.

Meanwhile, Trump released a new radio ad, that referenced Cruz's shot at "New York values" during a Republican presidential debate a week before New York's critical primary.

Cruz conceded that Trump will do well in upcoming primaries in the north east, including in Trump's home state of New York.

"He ought to win his home state convincingly," Cruz said, setting expectations high for Trump. "If Donald isn't substantially above 50 per cent in New York, it will be a big loss for him."

Cruz said he will fare better when the race shifts back west to Indiana, Nebraska, South Dakota and Montana, before finishing in California on June 7.

Associated Press writer Jonathan Lemire contributed reporting from New York. Bauer reported from Madison, Wisconsin.