ALBANY — New York is poised to establish one of the most expansive DNA databases in the nation, requiring people convicted of everything from fare beating to first-degree murder to provide samples of their DNA to the state.

On Tuesday, Gov. Andrew M. Cuomo and state lawmakers were putting the finishing touches on a deal to establish a so-called all-crimes DNA database, a move that is supported by all of the state’s 62 district attorneys and 58 sheriffs, as well as 400 police chiefs. New York already collects DNA from convicted felons and some people convicted of misdemeanors, but prosecutors say collecting DNA from all people convicted of misdemeanors will help them identify suspects of more violent crimes, and, in some cases, exonerate people wrongly accused.

“Every single time we’ve expanded the DNA database, we have shown how effective it is in convicting people who commit crimes, and we’ve also shown that it can be used to exonerate the innocent,” said Richard M. Aborn, the president of the Citizens Crime Commission.

Mr. Cuomo has made expansion of the DNA database a top priority for the year. His spokesman, as well as Lisa Hurst, a forensic DNA consultant with the firm Gordon Thomas Honeywell Governmental Affairs, said New York would be the first state to require all criminals to submit DNA samples. The spokesman declined to comment on the state of negotiations, but a senior administration official said negotiators were “very close” to a deal.

Lawmakers and officials briefed on the negotiations said the deal under discussion would allow defense lawyers, as well as prosecutors, access to the database. But they were still discussing the parameters of that access, and whether the database would be accompanied by other criminal justice measures intended to reduce wrongful convictions, as sought by the defense bar.

The developing agreement on the DNA database would be part of a series of pacts that would resolve many of the key outstanding issues in the legislative session this year, including the state’s budget for the next year, new political districts for state legislators and a new pension plan that would reduce retirement benefits for future public employees.

“We have the parameters of a deal,” Assemblyman Joseph R. Lentol, a Democrat from Brooklyn, said of the DNA bill that he is sponsoring.

Negotiations are moving at an unusually brisk pace in the capital, as Mr. Cuomo and lawmakers face two sets of deadlines: a federal court has demanded an update on the Legislature’s redistricting progress by Thursday, and the governor and legislators are required by law to have a new budget in place by April 1.

New York’s DNA database was created in the mid-1990s but applied only to those convicted of a limited number of crimes; the data collection has been expanded three times since then by the Legislature, most recently in 2006. Currently, DNA samples can be collected from people convicted of fewer than half of the crimes codified in state law, including all felonies and some misdemeanors. The measure would expand that to require that a DNA sample be submitted by all convicted criminals.

The Manhattan district attorney, Cyrus R. Vance Jr., an advocate for expanding the database, wrote in a recent opinion article that taking DNA samples from those convicted of low-level crimes had proved to be effective. He said that since the state allowed prosecutors to collect DNA from individuals convicted of petty larceny, investigators had been able to identify people linked to 48 murders and 220 sexual assaults statewide.

In one case prosecuted by Mr. Vance’s office, DNA from the butt of a cigarette smoked by Lerio Guerrero while he was being questioned for trespassing in Brooklyn last year linked him to a 1998 rape. Mr. Guerrero had been arrested several times in the interim, but none of his convictions were for crimes serious enough to warrant that he give a DNA sample.

Prosecutors also argue that the database could be used to exonerate the wrongfully convicted by matching DNA in their cases to someone else. But the defense bar has argued that courts sometimes place onerous restrictions on gaining access to evidence after a conviction and has, therefore, urged the Legislature to make it easier for defense lawyers to get evidence and run tests against the database.

“New York has a demonstrated problem with eyewitness misidentification and false confessions leading to wrongful convictions,” said Stephen Saloom, the policy director of the Innocence Project. “Any legislation that ignores the recommendations of those who’ve studied these issues is ignoring the heart of wrongful conviction reform needed in New York State.”

The Assembly speaker, Sheldon Silver, a Manhattan Democrat, has pushed to allow defendants access to the database. “We need to see fairness in terms of discovery, in terms of a defendant or a, quote-unquote, wrongfully convicted person,” he said.

The Senate majority leader, Dean G. Skelos, a Long Island Republican, said he was not opposed to access provisions, as long as it was “done in a very tight and controlled way.” Senator Skelos did say he was against including broader so-called wrongful conviction protections in the bill, like videotaping interrogations.

Some in the Assembly, led by Hakeem Jeffries of Brooklyn, have been pushing to include as part of the DNA bill a measure that would make it a violation, rather than a crime, to possess very small amounts of marijuana in public view, but it was not clear whether that provision would make it into the final language.

“There’s absolutely no justification for expanding the database and simultaneously including illegitimate misdemeanor marijuana arrest convictions that are racially biased and fatally flawed,” he said.

The discussions over the DNA database are running alongside quickening budget negotiations. As part of his spending plan, the governor is proposing to give newly hired public workers across the state, including in New York City, the choice between a less generous pension plan than is available to current employees or a defined contribution plan, which is similar to a 401(k).

But the senior administration official said the governor was now prepared to drop the 401(k) option, which has been a lightning rod for criticism from labor unions, so long as legislative leaders agreed to his proposal to create a new pension tier that would provide reduced retirement benefits for future workers.

Mr. Cuomo and lawmakers were also pursuing a compromise on redistricting that would allow legislative leaders to put in place their proposed district maps for the Senate and Assembly, but would create a bipartisan commission to redraw the state’s political map in the future, beginning after the 2020 census.