Several Democrats are claiming victory in key New York Senate races as their party aims for a veto-proof majority that would expand their control in the state's upper chamber.

Among the latest to declare victory is incumbent Democrat James Gaughran, who faced off against Republican challenger and attorney Ed Smyth in a closely watched race over a Long Island state Senate seat.

Smyth initially led among in-person votes, but Gaughran gained back ground with absentee ballots and eventually claimed victory, something Democrats have seen in other state Senate races, too.

"Those absentee ballots have come home to roost," said state Democratic Party chairman Jay Jacobs, acknowledging that in-person vote tallies initially did not look good for the Democrats.

"Winning reelection in a presidential year we always knew was going to be a very difficult feat. But we did it," said Gaughran, who is also an attorney.

In another critical race, Democratic incumbent Andrew Gounardes has claimed victory over Republican challenger Vito Bruno in the contest for a state Senate seat in southern Brooklyn.

"We face immense challenges in the months and years ahead," said Gounardes in a statement. "Housing, healthcare, economic, education, and food insecurities have manifested and been exacerbated by the pandemic."

Democrats Kevin Thomas and Anna Kaplan have also declared victory in their reelection bids for two state Senate seats on Long Island.

Thomas led Republican opponent Dennis Dunne by about 2,660 votes as of Wednesday in a race that garnered more than 149,000 votes, according to an unofficial vote tally. The Democrat trailed his opponent by thousands among in-person votes, but ended up making gains with absentee ballots.

Democrats hold 40 districts in the state's upper chamber and would need to pick up a net increase of two seats to reach a veto-proof majority.

Thomas issued a statement saying he was "deeply honored" to be reelected and looks forward "to continuing my efforts to build a stronger, fairer, more prosperous Long Island and New York State."

Absentee ballots, which have been thrust into the national spotlight this election cycle, have been an alternative way for people to cast their votes in the middle of the coronavirus pandemic.

At least 1.9 million people have returned absentee ballots in New York as of Nov. 13, according to data from the state Board of Elections.

Kaplan, who unlike Thomas led among in-person votes, had more than 77,800 votes as of Wednesday morning and was ahead of opponent David Franklin by about 15,600 votes.

Kaplan issued a statement Tuesday saying that Franklin had called her to concede the race.

"We had a nice chat, and I thanked him for his call and for running a spirited campaign," the Democrat said in the statement, commenting that she is "extremely humbled and grateful to the voters" in Nassau County.

Democrats are claiming victory in other state Senate races outside of Long Island as well.

On Wednesday, Democratic candidate Jeremy Cooney declared victory in the race for a state Senate district that covers part of Rochester, saying his campaign expanded its lead with absentee ballots in Monroe County being tallied.

Elijah Reichlin-Melnick, a Democrat candidate for a state Senate district in the Hudson Valley, declared victory Tuesday.

"We have a lot of work to do, and I look forward to going to Albany to fight for the middle class and working people of our district," he said in a statement.