''The governor made clear in our conversation his absolute intent to serve until Nov. 15, 2004. I accept that decision as final," Corzine said in a statement.
''In light of the governor's position, I want to make clear that my priority is to serve the people of New Jersey in the United States Senate."
Some Democrats had joined Republicans in urging McGreevey to resign before Sept. 3, the cutoff for holding a special election to complete the governor's term, which ends in January 2006.
Corzine, a Wall Street multimillionaire who has become an important fund-raiser for Democrats nationally, had seemed to be considering a run for governor. Fellow Democrats considered him a formidable candidate, but Corzine's statement could make it easier for McGreevey to stay in office until November.
If McGreevey does not resign by Sept. 3, the remainder of his term will be filled by state Senate President Richard J. Codey.
Meanwhile, a major contributor to McGreevey pleaded guilty yesterday to charges stemming from a scheme in which he allegedly hired a prostitute to seduce his brother-in-law, a witness in the case.
Real estate mogul Charles Kushner pleaded guilty in federal court to 18 charges, including retaliating against a federal witness and violating campaign finance laws.
McGreevey was not implicated in the charges, but the Kushner case was one of a series of scandals that clouded the governor's future long before he announced his resignation last week.
''Mr. Kushner's case has absolutely nothing to do with Governor McGreevey," Kushner's lawyer, Benjamin Brafman, said outside court.
Kushner also pleaded guilty to 16 counts of filing false tax returns through various real estate partnerships.
Kushner had been under federal investigation for about three years on the campaign contribution and tax fraud charges. He then was accused of hiring a prostitute to have sex with his brother-in-law, William Schulder.
Prosecutors said Kushner ordered the sex act videotaped and a copy of the tape sent to his sister, Schulder's wife, who was cooperating in the investigation. Prosecutors said Kushner's aim was to retaliate against the family for cooperating with the government.
US Attorney Christopher J. Christie said Kushner faces 1 to 2 years in prison and ''substantial" fines. The plea deal does not require Kushner to cooperate with investigators, and Christie said he did not expect Kushner to do so voluntarily.
Brafman said Kushner accepted responsibility and will be stepping down as chairman of his $1 billion company.
The plea was made six days after McGreevey announced his affair with a man and intention to resign Nov. 15. Sources close to McGreevey have identified the man as Golan Cipel, an Israeli who held a state homeland security job in 2002.
While the guilty pleas entered yesterday are not related to the McGreevey case, Kushner sponsored the work visa that allowed Cipel to come to the United States and gave him a $30,000-a-year job in public relations with one of his companies.
Cipel says he is heterosexual and has accused McGreevey of sexual harassment.
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