New York (CNN) -- Troubled New York Democratic Gov. David Paterson, who recently abandoned his quest for a full term, said Monday he will not resign his office.
He also asserted that he retains enough authority to effectively govern one of the country's largest states for his remaining 10 months in power.
Paterson announced Friday that he would not run for a full term. His announcement came in the wake of news reports that one of his top aides was involved in a domestic violence incident with a woman and that state police later pressured the woman to keep quiet.
Paterson has asked New York Attorney General Andrew Cuomo, a possible Democratic contender for the governor's office, to investigate the matter.
"I would think [resignation is] off the table," Paterson said at a question-and-answer session with reporters sponsored by the New York Observer. "In terms of authority of power, I have the power."
"There is a hysteria I have been the victim of the past month. ... I find the whole discussion to be very remote from the issues we are facing right now," Paterson said.
New York, like many states, is facing a major budget crisis as a result of the economic downturn.
Paterson said Friday that it "has become increasingly clear ... that I cannot run for office and try to manage the state's business at the same time."
He denied any wrongdoing, however, claiming that he has "never abused [the governor's] office, not now, not ever."
Paterson has suspended the aide accused of domestic violence, David Johnson, without pay. He said Friday that he is looking forward to a full investigation of his and his administration's actions.
Johnson, a onetime driver for Paterson, has been accused of several acts of wrongdoing in a series of stories by The New York Times. He has not been charged with a crime. Efforts to reach him and his attorney have been unsuccessful.
The New York Times recently reported that New York State Police contacted the woman who allegedly accused Johnson of domestic violence to encourage her to abandon efforts to seek a protective order against him. The newspaper quoted Lawrence Saftler, a lawyer for the alleged victim, whom the newspaper did not identify. Saftler did not return calls from CNN.
The newspaper also reported that the state police confirmed the woman was visited by a member of the governor's personal security detail.
Paterson said Monday that "over the past month there have been hideous rumors [and] none of those stories came to fruition."
In a statement released Thursday, the state police said Cuomo requested that the agency not conduct an internal investigation into the matter.
"The state police will fully cooperate with the attorney general's office and their investigation," the statement said.
Paterson told reporters Monday that he thinks Cuomo "can conduct this investigation fairly."
On Thursday, New York Deputy Secretary for Public Safety Denise E. O'Donnell abruptly resigned amid the burgeoning scandal surrounding Johnson's alleged abuse.
In announcing her resignation, O'Donnell noted that "the fact that the governor and members of the state police have acknowledged direct contact with a woman who had filed for an order of protection against a senior member of the governor's staff is a very serious matter," and called such actions "unacceptable regardless of their intent."
She said State Police Superintendent Harry Corbitt told her in January that a senior administration staff member had had an argument with his girlfriend and a domestic incident report was filed.
Corbitt told her "the matter was being handled as a local police matter by the New York Police Department" and her state police were not involved, O'Donnell said. She said she resigned after learning state police were in fact involved.
Corbitt said he did not dispute O'Donnell's account of what he told her, but said "the conclusions she appeared to draw from these statements were incorrect."
The New York Times has previously reported on other allegations of wrongdoing by Johnson when he was a teenager.
The newspaper said it based its story on "interviews and records."
Paterson had defended Johnson before the most recent allegations. Earlier this month he told CNN that The New York Times chose to "splash" Johnson's "youthful offenses across the pages of its newspaper. ... I profoundly believe in this principle of redemption and giving young people a second chance."
Paterson became governor in 2008, after a sex scandal prompted then-Gov. Eliot Spitzer to resign. Paterson is New York's first African-American governor and the fourth in U.S. history.
The governor is legally blind, and although documentation is scarce, it is widely believed that he is the nation's first blind governor.
He was first elected to the New York State Senate in 1985, representing the 30th District, encompassing Harlem, East Harlem and the Upper West Side of Manhattan.
In November 2002, Paterson was elected New York Senate minority leader.
CNN's Julian Cummings contributed to this report.