The U.S. contests for the Republican and Democratic presidential nominations have turned into contentious fights for delegates to the parties' national conventions, where the candidates for November's national election will be picked.
Billionaire real estate mogul Donald Trump is the Republican front-runner, but he complained Monday that party officials have created a "crooked, crooked system" to keep him from winning a first-ballot victory at the party's July convention in Cleveland, Ohio.
While Trump has won the most state-by-state nominating contests, he is well short of a majority of convention delegates needed to claim the nomination.
"The system, folks, is rigged," Trump told a rally in New York, where both parties are holding primary elections April 19. "It's a rigged, disgusting, dirty system."
Trump's ire was aimed at weekend voting in the western state of Colorado, where his chief rival, Texas Senator Ted Cruz, collected all 34 of the state's national convention delegates at a political meeting confined to party activists, not voting open to rank-and file Republicans or the general public, as has been the case in other states.
U.S. Republican presidential candidate John Kasich attends a campaign event at the Women's National Republican Club in the Manhattan borough of New York, April 12, 2016.
Cruz scoffed at Trump's complaint, telling supporters in California, "Donald, it ain't stealing when the voters vote against you. It's the voters reclaiming this country and reclaiming sanity."
Republican National Chairman Reince Priebus also dismissed Trump's attack, saying, "The rules were set last year. Nothing mysterious, nothing new. The rules have not changed."
At the moment, Trump, a brash, one-time television reality show host, has 775 of the 1,237 national convention delegates he needs to claim the Republican nomination before the quadrennial event starts, compared to 545 for Cruz and 143 for Ohio Governor John Kasich.
Here is an estimated delegate count for each candidate:
Donald Trump: 898
Ted Cruz: 560
John Kasich: 153
Hillary Clinton: 1,997
Bernie Sanders: 1,238
Total delegates needed for party nomination:
* As of April 27, 2016
But to reach the 1,237 figure, a bare majority of convention delegates, Trump would have to win nearly 60 percent of the delegates yet to be chosen in the state contests that extend through early June, a higher ratio than in the victories he has recorded so far.
U.S. political analysts are widely suggesting that if Trump does not win a first-ballot victory at the national convention, he will not win the nomination at all, with many of his delegates abandoning him in subsequent ballots, possibly handing the nomination to Cruz, a conservative firebrand in the halls of Congress in Washington.
Some Republican delegates say they are concerned that numerous national polls in the U.S. show both Trump and Cruz losing the November election to the leading Democratic contender, former Secretary of State Hillary Clinton, although Cruz fares better against her.
Delegates pledged to Trump based on the voting in the state contests are generally committed to vote for him on the first convention ballot, but can change their mind and vote for another candidate on the second and later ballots until someone reaches the 1,237 figure.
Trump, who lives in a luxury high-rise building in New York, has a wide lead in his home state in pre-election surveys over both Kasich and Cruz, and also leads in several states set to vote April 26. But it is unclear, even if he wins these contests, whether he will be able to claim enough national convention delegates to give him a first-ballot majority.
Kasich, without naming either Trump or Cruz, attacked their policies Tuesday as divisive, telling a group of Republican women in New York that his opponents are "not worthy of the office they are seeking."
Some Republican figures say they want their national convention to nominate someone other than the three remaining candidates.
One possible alternative choice, Republican House Speaker Paul Ryan, called a news conference for later in the day to rule himself out. Ryan was the party's losing vice presidential candidate in 2012.
Clinton, the country's top diplomat from 2009 to 2013, has a wide convention delegate lead over her sole challenger, Vermont Senator Bernie Sanders, but also has yet to reach a majority.
She has 1,786 convention delegates of the 2,383 she needs to claim the nomination, compared to 1,107 for Sanders. But Sanders, who waged a tough campaign against Clinton's connections to Wall Street financiers, has won seven of the last eight state contests, giving him some momentum heading into the New York contest.
Polls, however, show Clinton with a wide lead over Sanders in New York, her adopted home state where voters twice elected her to the Senate.
Clinton, seeking to become the first female president in the U.S., said she expects to have enough convention delegates pledged to her ahead of July's Democratic national convention.