(CNN) The Republican Party's already volatile 2016 presidential campaign was roiled anew Tuesday when all three Republican candidates backed away from a pledge to support the GOP nominee.

With rising anger between rival campaigns ripping at an already fragile Republican Party, Donald Trump, Ted Cruz and John Kasich all declined to say they would unquestionably support the candidate who emerges as the GOP standard-bearer in November's election.

It was the latest sign of chaos and division in the GOP as the race turns to Wisconsin's crucial April 5 primary and the increasingly desperate anti-Trump forces try to halt his march to the nomination.

The pledge was introduced last year amid fears that Trump could bolt the Republican Party if he failed to win the nomination and mount an independent bid if he believed that he wasn't treated well by party leaders. GOP leaders feared that such a move would automatically hand the general election to Democrats.

But the party's paper-thin unity strained by Trump's anti-establishment campaign has led to the possibility of a contested convention. Such a scenario threatens to tear the party apart and could make Trump's legions of supporters feel angry and disenfranchised if the billionaire wins with most delegates in the primaries but is deprived of the nomination.

Asked by moderator Anderson Cooper at CNN's town hall about the pledge and whether he would support the eventual nominee regardless of who it was, Trump responded, "no."

"I have been treated very unfairly," Trump said, hitting out at the "RNC, the Republican Party, the establishment." He also said that he is not looking for chief rival Cruz's support either.

"He does not have to support me," he said. "I am not asking for his support."

Cruz, who preceded Trump at the town hall, hedged when asked whether he would support Trump if he became the Republican nominee.

"Donald is not going to be the GOP nominee. We are going to beat him," Cruz said, though he did not categorically refuse to back the billionaire.

He did, however, add that nominating the current party front-runner would be a "train wreck" and hand the White House to Democrat Hillary Clinton.

And Kasich said that in retrospect it would probably have been wiser if none of the candidates in the first place had made the promise to support the nominee no matter what.

"I have got to see what happens," Kasich said. "If the nominee is somebody I think is really hurting the country and dividing the country, I can't stand behind them."

But Kasich would not spell out whether he thought of Trump as somebody that was hurting the country.

Trump discusses campaign manager charges

Trump at the town hall also addressed the simple battery charge that has been brought against his campaign manager, standing by the aide and mocking the reporter who brought the complaint, saying she had changed her story about the incident.

Trump said he would not fire the aide, Corey Lewandowski and disputed the woman's initial account of the incident earlier this month in which she said she almost fell to the ground.

"She's not a baby. In her own words, 'I was jolted backwards' ... She wasn't 'yanked down,'" Trump said, referring to a statement made by the reporter Michelle Fields, who worked at the time for Breitbart News, which he said was not reflected in scenes shown on a security tape that has since emerged.

Addressing the incident involving Fields, Trump alleged that she was in fact pushing Trump as he tried to leave a press conference and was brandishing a pen, which he said could have alarmed Secret Service agents protecting him.

He said that Lewandowski had been "unjustly accused."

"It would be so easy for me to terminate this man, ruin his life, ruin his family ... and say you are fired. I have fired many people, especially on 'The Apprentice,'" Trump told moderator Anderson Cooper. "The problem is everybody dumps people when there is a sign of political incorrectness."

In contrast, GOP opponent Ted Cruz said earlier at the town hall that he would "of course" ask his campaign manager to resign if he were charged with battery.

"It shouldn't be complicated," Cruz said. "Members of the campaign staff should not be physically assaulting the press."

He added, "I will say it is consistent with the pattern of the Trump campaign. The culture of the campaign has been a campaign built on attacks and insults."

Ohio Gov. John Kasich, the final candidate to appear at the town hall, was also asked whether he would fire Lewandowski.

"Of course I would," he said.

The charges against Lewandowski have prompted fresh criticism of Trump's campaign and came a week ahead of the Wisconsin primary, which is shaping up as a huge night in the bid by the billionaire's rivals to deprive him of the GOP nomination.

Trump, Cruz spar over wife remarks

The feud between Trump and Cruz turned even more personal last week when the real estate mogul took aim at the Texas senator's wife.

Cooper at one point challenged Trump for tweeting what appeared to be an unflattering picture of Cruz's wife Heidi, after a super PAC that the billionaire accused of working with Cruz used a revealing picture of his wife, Melania, a former model. There's no evidence, however, that the super PAC worked with Cruz, which would be illegal.

"I didn't start it," Trump, said.

Cooper replied, "Sir, with all due respect, that is the argument of a five-year-old."

"I didn't start it," Trump insisted, adding that he would prefer to talk about nuclear proliferation than candidates' families.

Cruz also argued that the Trump campaign was behind a salacious report published in the National Enquirer that alleged the senator had multiple extramarital affairs. But he said he wanted to discuss issues with the billionaire.

"What I am not interested in doing is what Donald's pattern has been. It's personal attacks, it's attacking family members," he said.

Last week, Trump took exception to an ad by a super PAC unaffiliated with Cruz featuring a risque picture of his own wife, Melania, a model, and threatened to reveal unspecified information about Heidi Cruz, prompting a furious response from the Texas senator.

Foreign policy

On the foreign policy front, Trump also then went on to defend his statement that Japan and South Korea should consider developing nuclear weapons to defend themselves from North Korea rather than relying on the U.S. nuclear umbrella.

Experts have warned that such a move could result in an arms race in Asia and elsewhere. But Trump said that America could no longer afford to be solely responsible for defending its allies.

"Maybe it is going to have to be time to change," he said.

Kasich, however, took issue with Trump's statement that NATO is "obsolete" because it was set up to combat the Soviet Union, a threat that no longer exists.

"That's absurd" Kasich said, getting a smattering of applause. But the Ohio governor said that Washington would always want its allies to do more and blamed too much "socialism" and political correctness for shortcomings among American partners.

The delegate race

Trump also complained that in the state of Louisiana, which he won, he appears to have been awarded fewer delegates than Cruz due to the vagaries of election law.

"I won the election, and then it is all about the delegates," Trump said. "Then I find out that I got 10 delegates less than the guy that lost. I beat him," Trump said.

Cooper challenged Trump, saying that the Louisiana developments were well within the rules and suggested that it was all down to a superior ground game by the Cruz campaign.

"I don't call it ground game. I call it bad politics," Trump replied.

Kasich has maintained that he's the only adult in the GOP race and, despite having won only one primary to date, the sole remaining Republican who could emerge from a possible contested convention to beat Clinton.

Kasich said that he would refuse to stoop to the levels of campaign rhetoric that he blamed Cruz and Trump for adopting. Asked about a tweet by a senior campaign aide that was critical of the Texas Senator, Kasich disavowed it.

"Sometimes, he gets a little tweet-happy, and I don't like that, and I will have a word with him about it." Kasich said of his aide.

Cruz earlier in the night ruled out any alliance with Kasich to maximize their chances of stopping Trump. Such an arrangement could in theory force the Republican front-runner to face only one candidate in each state for the rest of the campaign and coalesce opposition against him, complicating his hopes of winning the 1,237 delegates needed to claim the nomination.

"It makes no sense at all. John Kasich has no path to winning. We are competing to win, we are not competing to stop Trump. John Kasich went 0 for 27. He lost 27 states in a row," Cruz said.

Cruz said his "preferred option" was to win 1,237 delegates, though he said it was entirely possible that a contested convention could unfold if no one reached that number. But he argued that the only two names on the ballot in that situation would be himself and Trump.

Cruz defends comments on monitoring Muslims

The Texas senator was repeatedly asked to justify his call last week after the Brussels terror attacks for greater surveillance of Muslim neighborhoods in the United States.

Cruz said that he took it as a badge of honor that President Barack Obama, Clinton and New York police authorities had attacked him after he made the comment, despite their claims that such programs had not worked in New York City.

"If you want to stop radical Islamic terrorism, the answer is not to go hang out in random neighborhoods, it is instead to focus on communities where radicalization is a risk," Cruz said, before suggesting that Democrats and political correctness would consign the U.S. to the same problems in enforcing law in Muslim communities that he said Europe faces.

"America should not make the same mistakes as Europe," he said. "We should have law enforcement actively engage to stop radicalization."

But Kasich hit out at Cruz's call for more police patrols in Muslim neighborhoods, saying it would alienate the very people that authorities need to help combat extremism.

"If you polarize the entire Muslim community, how are you going to get the information that you want?" Kasich asked. "The vast, vast majority of Muslims -- they think that their religion is being hijacked."

In a more personal moment, Cruz, who has angered some of his colleagues in Washington with his uncompromising tactics, was asked by a member of the audience to describe his greatest failure and what he had learned from it.

"I'm a pretty driven guy," Cruz answered, saying he had a passionate commitment to free market economics and the Constitution. "At times, I am hard-charging, I have stepped on some toes ... maybe I should have pulled back some in some circumstances ... it is a strength and a weakness."

Both Kasich and Cruz need a big victory over Trump to secure most if not all of Wisconsin's 42 Republican delegates next week. They are trying to stop the former reality TV star short of the 1,237 delegates needed to win the nomination outright and open the way to a contested convention.

But the fact that they are both competitive in Wisconsin risks splitting opposition to Trump, allowing him to march on to more favorable contests next month in the Northeast with his large delegate lead untrimmed.