Presidential candidates Donald Trump and Ben Carson said Sunday that talk of a contested convention to select the Republican nominee violates terms of neutrality agreements they made with party leaders not to mount third-party campaigns.

Trump said that party leaders need to "get used to" his being in the race, and that he hopes reports that party officials gathered recently to discuss contesting his nomination - even if he receives the required number of delegates - are incorrect.

"I've been hearing about these closed-door meetings and I don't like that," Trump told CNN host Jack Tapper on State of the Union. "That wasn't the deal I made. I signed a pledge, and the pledge was supposed to be a double deal. They were supposed to be honorable, so we're going to find out. If it's going to be that way we'll have problems."

The last so-called brokered convention in U.S. politics took place in 1952, when then-Illinois Gov. Adlai Stevenson was drafted by the Democratic Party as a compromise candidate when no one else gained enough support to secure the nomination. Stevenson lost in the general election to Republican Dwight D. Eisenhower.

A crowded Republican field for 2016 with more than a dozen hopefuls has meant Trump, along with Carson, Sen. Ted Cruz and others, have competed for a fractured party base.

On Fox News Sunday, the real estate mogul lashed out at Cruz, who has taken a 10-point lead over Trump, 31 percent to 21 percent, among Iowa Republicans, according to a new Bloomberg Politics/Des Moines Register poll. (The poll of 400 likely caucus goers was conducted Dec. 7-10 and has a 4.9 percentage point margin of error.)

Trump said Cruz doesn't have the temperament or judgment to be president, and has acted in the Senate "like a little bit of a maniac."

Carson, a retired neurosurgeon with no political experience who also has shown a strong presence in the race for the party's nomination, renewed his threat to leave the party if a brokered convention designed to blunt his standing were to take place.

"One of the reasons that I got into this is because I heard the frustration in the people who are so tired of backroom deals, of subterfuge, of dishonesty," Carson said during an appearance on ABC's This Week with George Stephanopoulos. "And, you know, if that is the case, then, you know, I'm out of here."

The Washington Post reported Thursday that 20 Republican Party stalwarts discussed the possibility of brokering the convention at a Washington dinner held by Republican National Committee Chairman Reince Priebus. A person who attended the dinner confirmed to Bloomberg that it took place, and that Priebus, members of Congress, establishment lobbyists, and others have held similar discussions for weeks.

Carson said he's spoken to Preibus and was told that the meeting was a routine one and there are no backroom deals taking place. "But, you know, the jury is out. We'll certainly be keeping a close eye on things," he said.

Trump said he agrees with Carson's positions.