The event at Elizabeth City Hall marks the New York senator's first campaign appearance in New Jersey, a Democratic-leaning state that twice gave its electoral votes to her husband, Bill Clinton, in his successful presidential bids.
More recently, a majority of state voters backed the failed runs of Democrats Al Gore and John Kerry.
On Monday Clinton told the crowd of about 400 that if elected, she would pursue universal health care and energy independence.
"I'm running for president because I want to get back to setting goals for our country," Clinton said.
Corzine, who served in the Senate with Clinton before becoming governor in 2006, called her "remarkable."
"I'm proud to say that if George Bush hasn't brought us out of Iraq, she will," Corzine said.
The event took place nearly 10 months before New Jersey holds its primary elections on Feb. 5, a change from its traditional date in June. New Jersey is among several states that will be among the first primaries, including giants such as California, Florida, New York and Texas.
A Qunnipiac University poll in February had Clinton with 41 percent of the vote in a New Jersey Democratic Party primary, compared to 19 percent for Illinois Sen. Barack Obama.