At least 34 percent of eligible registered voters cast ballots, the highest primary election turnout since 1952, when 39 percent voted.
The highest turnout for any primary in New Jersey was in 1928, a presidential year, when 54 percent of registered voters cast ballots.
The last presidential primary, in 2004, which also included U.S. House candidates, attracted 9 percent of registered voters.
Sen. Hillary Rodham Clinton beat back a strong challenge by Barack Obama to win the Democratic primary in her adopted state.
Sen. John McCain defeated Massachusetts Gov. Mitt Romney to claim all 101 of New York's Republican delegates.
With 38 percent of precincts reporting, Clinton had 60 percent of the vote to Obama's 37 percent. McCain had 51 percent, compared with Romney's 28 percent.
Although Clinton won New York, Obama seemed poised to get a big chunk of New York's 232 Democratic delegates because many are split based on the votes in each of the state's congressional districts.
Clinton was tested by Obama in heavily black neighborhoods in New York City and liberal upstate stretches and on college campuses across the state.
New Jersey Voting Prolems
New Jersey officials said Tuesday that they were getting more complaints than usual about problems at polling places - including some early-morning confusion at Gov. Jon S. Corzine's polling place.
Michael Harper, clerk to the Hudson County Board of Elections, said that when the first voter arrived at the Hoboken fire station where Corzine votes, an election worker did not press the right buttons to set the machine.
The worker called the Board of Elections, which talked her through the problem, Harper said. He said the worker was confused because different buttons are used for the primary election than in other elections.
Some media reports said that Corzine, who has endorsed U.S. Sen. Hillary Clinton, could not vote because of the problem. But his spokesman, Jim Gardner, said the governor was running late for other reasons and voted around 6:50 a.m - about a half-hour later than scheduled.
Harper said when the governor did vote, he was in and out of the polling place in 2 1/2 minutes and was the 14th person to vote on that machine.
Harper said another voting machine in the same firehouse was accidentally turned off soon after voting began at 6 a.m. and another machine had to be brought in to replace it.
That meant that for less than a half-hour, two machines were out of service in the same firehouse. The American Civil Liberties Union of New Jersey has complained that provisional ballots were not handed out to voters who could not vote because of the problems.
Laurie Brewer, a spokeswoman for the state Public Advocate's office, said the office was getting more calls from voters with complaints on Tuesday than it did during general elections last November.
She said many of the calls are coming from voters who are frustrated that they cannot switch parties for the primaries and from voters registered as independents who are being turned away. Only party members may vote in the primary, though independent voters can join parties at the polling place.
Deborah Jacobs, director of the ACLU of New Jersey, said an officer in her group spotted an electioneering problem when he went to vote at a Montclair school: student-made signs for some, but not all, candidates were hanging near the voting booths.
Under New Jersey election laws, no material supporting candidates is allowed within 100 feet of polling places.
Jacobs said people had called her group with a smattering of other complaints, too, such as people not being offered provisional ballots in Jersey City, a woman with a baby stroller being unable to get into a Hoboken polling site, a Democrat in Monmouth County being given a machine set up for Republicans, among others.