New Yorkers turned out Tuesday for the state's presidential primary elections.

Donald Trump was quickly declared the winner on the Republican side, just after 9 p.m., although final vote tallies were not yet available. He bested Texas Sen. Ted Cruz and Ohio Gov. John Kasich.

Hillary Clinton claimed victory on the Democratic side.

Mayor Bill de Blasio and former Mayor David Dinkins praised Clinton in front of a crowd at her campaign headquarters before she took the podium.

De Blasio credited Clinton with putting forth "the most progressive platform for economic change."

Gov. Andrew Cuomo also took the stage.

"How great was it to have Hillary and Bill back in New York campaigning?" Cuomo asked the crowd before recalling his work for former President Bill Clinton's administration in the 1990s. "Hillary is a New York Democrat. She gets us."

The governor cited New York's gun control laws, educational funding and recent paid family leave and $15 minimum wage laws.

"In New York state, we don't just talk the progressive talk, we walk the progressive walk," Cuomo said. 

Clinton took the stage with the Jay-Z song, "Empire State of Mind" playing as supporters cheered.

"There's no place like home," she said. "New Yorkers, you've always had my back, and I've always tried to have yours."

Clinton made a brief appeal to supporters of rival Bernie Sanders, saying they shared a good deal of common goals, but also called her own proposals more realistic.

"Imagine a tomorrow where no barriers hold you back, and all of our people can share in the promise of America," she said.

Speaking at Trump Tower in Manhattan shortly after the election was called, Trump thanked cheering supporters.

"It's really nice to win the delegates with the votes," Trump told supporters. "Nobody should be given delegates, which is a ticket to victory, but it's not a fair victory. Nobody should take delegates and claim victory unless they get those delegates with voters and voting."

"It's a crooked system," Trump said of the possibility of a contested GOP National Convention. "It's a system that's rigged. We're gonna go back to the old way, which is you vote -- you win."

He also promised to negotiate "unbelievable" trade deals to bring jobs back to the country and pledged to build up U.S. military power.

The primary process for the Republicans and for the Democrats is slightly different.

For the Republicans, voters only have to choose their candidate. Due to a missed deadline, Dr. Ben Carson's name remained on the ballot even though he's out of the race.

For Democrats, voters must choose a candidate and then the pledged delegates to send to the party's national convention.

The number of delegates Democratic voters must choose varies by their district.

Voters not registered in the Democratic or Republican parties are not allowed to vote in those primaries due to the state's closed primary system.