Two alleged burglars who were caught trying to saw their way into a bank early yesterday morning are being investigated for two more attempted bank burglaries that happened in the last three months, prosecutors said.

The suspects, Fred Piro, 41, and Louis Spano, 45, were remanded for three days while federal investigators try to link them to the attempted robberies, one that happened at the same Independence Bank that they allegedly attempted to burglarize yesterday. Bail was set at $1.25 million for both suspects, but they won’t be able to leave jail until a hearing on May 18 about any evidence linking them to the other robberies.

The men were caught trying to flee the bank’s roof at about 12:30 a.m. yesterday, according to the criminal complaint filed in the Eastern District of New York federal court. A silent alarm was triggered on the roof of the bank at 83-20 Roosevelt Ave. in Jackson Heights at about midnight. A guard from the security company and a police officer responded to the scene. Surveying the inside of the bank, they could hear a loud drilling noise and smell something burning, investigators said.

The uniformed officer immediately radioed for assistance, and additional units formed a perimeter around the bank.

One officer from the neighboring 115th Precinct got up on a shed to see the roof, where he spotted Mr. Spano carrying a black duffle bag, according to the complaint.

The officer shouted at him not to move, but Mr. Spano knocked the duffle bag into the hole in the roof and tried to flee, according to the complaint. Mr. Piro emerged from the hole carrying a walkie-talkie, which he threw into an alley off the roof, the complaint said.

The officer and guard inside the bank had meanwhile spotted one of the men in a crawlspace above the bank’s massive vault, and were making their way to the roof. They chased Messrs. Piro and Spano, who were trying to get through a hole in a chainlink fence separating the bank’s roof from a neighboring social club. Mr. Spano’s sweater was caught in the barbwire, and the two were arrested by police officers.

Because the men were attempting to enter a bank vault, the case was transferred to the FBI’s Joint Bank Robbery Task Force.

In the duffle bag, police found all the elements of a cinematic heist: hammers, an electric saw, ropes, a walkie-talkie, and kneepads.

Outside Brooklyn federal court, Mr. Spano’s lawyer, Charles Emma, said his client was in the vicinity of the bank last night but innocent of attempted burglary. Asked what his client was doing in the area, Mr. Emma said he didn’t know. Mr. Piro’s lawyer, Harold Levy, couldn’t be reached for comment.

The federal prosecutor, James Loonam, told Judge Cheryl Pollak that the two men should be held without bail because they were being investigated for two other attempted bank robberies and because of their criminal records. Mr. Piro is out on bail after allegedly making a bomb threat in Florida and Mr. Spano has two outstanding warrants in New Jersey, for assault and domestic violence.

“The strength of evidence of this case is overwhelming,” Mr. Loonam said. “They were basically caught redhanded.”

Mr. Spano is a manager at New York One Shipping Company in Brooklyn, his lawyer, Mr. Emma said. He lives with his mother and his three children. Mr. Piro owns a company called Cityview Contracting and rents apartments in a building he owns on President Street in Brooklyn.

“I guess I’m just kind surprised because my impression of the family is that they’re already millionaires,” a woman who knows Mr. Piro said after hearing of the arrests yesterday. Mr. Piro is married and has a son.

One of the robbery attempts investigators are looking into happened on the same roof of the Independence Bank back in March. The would-be burglars cut a hole into the staff kitchen instead of the vault. Bank officials added hidden sensors to the roof after the attempt, and it was those sensors that triggered the alarm yesterday. A similar attempt was made at a nearby bank in April, prosecutors said.

“Things worked just like they were supposed to,” a spokesman for the bank, Michael Armstrong, said. “They pierced the roof, the alarms went off, and the police came and caught them.”