Representative Max Rose, the Staten Island Democrat who was soundly defeated last month in his bid for a second term, signaled on Thursday that he plans to enter an already crowded field in the 2021 mayor’s race in New York City.

The evidence of Mr. Rose’s intentions came in a bare-bones filing with the city’s Campaign Finance Board indicating that he had formed a mayoral campaign committee.

Neither Mr. Rose nor anyone associated with him returned calls seeking comment on the filing. But the congressman did post a cryptic message on Twitter at around 7:30 p.m. that appeared to telegraph an imminent announcement.

He cited Taylor Swift, who announced on Thursday that a new album was forthcoming, saying that the singer was “not the only one previewing news tonight.”

“Stay tuned NYC!” he added.

The social media tease notwithstanding, Mr. Rose’s filing brought him a significant step closer to vying to become the next mayor of a city that is facing huge challenges caused by the pandemic and the financial crisis it touched off.

Several of his congressional allies had suggested they expected him to join the race after losing his re-election bid to Nicole Malliotakis, a Republican member of the State Assembly, in a district that encompasses parts of South Brooklyn in addition to Staten Island — the city’s most conservative congressional district.

Ms. Malliotakis, who has been resolute in her support for President Trump throughout his term and re-election campaign, claimed 53 percent of the vote to Mr. Rose’s 47 percent. And although The Associated Press did not declare her the winner until Dec. 1, Mr. Rose had conceded defeat two weeks earlier.

Mr. Rose had been far more reluctant himself to criticize Mr. Trump than many of his Democratic colleagues. In April, he went so far as to say that it would be all right with him if the president won re-election if it was because he had reined in the pandemic. He also initially opposed the move to impeach Mr. Trump, but ultimately voted for impeachment.

In a nod to the district’s conservative tilt, Mr. Rose, who won election in 2018 by a margin similar to the one he lost by this year, effectively ran his centrist campaign against two opponents: Ms. Malliotakis and Mayor Bill de Blasio.

He did not waste words in criticizing Mr. de Blasio, referring to his fellow Democrat in a memorable six-second ad as “the worst mayor in the history of New York City.”

Mr. Rose also attended a June demonstration on Staten Island to protest the police killing of George Floyd. Ms. Malliotakis made his participation in the event a focal point in the campaign as she sought to cast him as supporting calls to “defund the police” in a district that is home to many law enforcement officers.

He said he had taken part in the protest as a gesture of unity, and stood by his decision to do so on election night even as defeat loomed.

Mr. Rose, 34, is among several well-known Democrats who have been rumored to be considering joining a field that already includes more than a dozen candidates, with nearly half viewed as potentially serious contenders.

Others who may be set to enter the fray include Andrew Yang, a technology entrepreneur who ran unsuccessfully for the Democratic presidential nomination this year, and Christine Quinn, the former City Council speaker, who placed third in the Democratic mayoral primary in 2013.

It is unclear how Mr. Rose’s political persona would play in the mayoral campaign. His positions were on the liberal side for his district but might not be liberal enough to win over a plurality of mainstream Democrats in a citywide primary.

On the flip side, several leading candidates are already battling for those voters, and Mr. Rose, a U.S. Army veteran who served in Afghanistan, might appeal to more conservative voters who consider law and order a priority at a time when homicides and shootings are rising in the city.

One quality that he would bring to a race that will most likely be expensive is a proven ability to raise money: He collected, and spent, more than $9 million for his re-election campaign, federal campaign finance filings show.

Mr. Rose’s filing came amid a flurry of activity in the race, arriving the same day that another Democratic mayoral hopeful, Kathryn Garcia, the city’s former sanitation commissioner, formally announced her candidacy, and two days after Shaun Donovan, a former top housing official in the Obama administration, did the same.

They and the other contenders are competing to lead a city that is in the midst of one of its most wrenching and consequential periods in recent history.

The coronavirus, which has already been linked to the deaths of more than 24,000 residents, is surging again. On Staten Island, emergency hospital beds were added in November to handle a spike in virus cases.

Katie Glueck contributed reporting.