WASHINGTON — Boston officials said today the Tsarnaev brothers were prepared to launch more violent attacks before their odyssey of terror was disrupted last week — given the large quantity of explosives and ammunition they possessed — but that all evidence thus far indicates they were acting alone and were not part of a broader conspiracy.

“All of the information I have is they acted alone, these two individuals, the brothers,’’ Mayor Thomas M. Menino said on ABC’s “This Week.’’

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“The older brother’s dead now. We have the second one ... in very serious condition,’’ he said. In an apparent reference to his medical condition, he added, “We don’t know if we’ll ever be able to question the individual.”

Menino’s comment only fueled more questions about the medical condition of the younger suspect, Dzhokar Tsarnaev, who is listed as as serious but stable at Beth Israel Deaconess Medical Center with undisclosed injuries.

On Saturday, Governor Deval Patrick said the young man was not able to be interviewed. Speaking on “This Week’’ today, Senator Dan Coats of Indiana, a member of the Senate Select Committee on Intelligence Committee, said, “The information we have is that there was a shot to the throat, and it’s questionable when and whether he’ll be able to talk again.  Doesn’t mean he can’t communicate.  But right now I think he’s in a condition where they can’t get any information from him at all.”

Menino and other top Massachusetts officials fanned out across the Sunday talk shows to discuss the aftermath of Monday’s Boston Marathon bombings, the worst terrorist attack in the United States since 2001, and where the investigation may go from here.

Boston Police Commissioner Edward F. Davis said he believes Dzhokhar and his older brother Tamerlan Tsarnaev, who was killed in an exchange of gunfire early Friday morning in Watertown with police, were armed for another rampage following the Monday bombing attacks.

“They had IEDS,” Davis said on CBS News’s “Face the Nation,’’ referring to improvised explosive devices. “They had homemade hand grenades that they were throwing at the officers. The scene was littered with unexploded improvised explosive devices that we had to point out to the arriving officers,” including one in the abandoned SUV the brothers had allegedly stolen.

Davis said today that federal authorities are trying to trace the origin of the firearms and explosive devices employed by the two suspects. “We hope to try to find out exactly where they obtained” the arsenal, he said.

Asked about any further threat to the public, Governor Deval Patrick, also appearing on “Face the Nation,’’ said “all of law enforcement feels it is over. … You can feel the relief here at home.”

On NBC’s “Meet the Press,’’ Patrick said surveillance video showed Dzhokhar Tsarnaev dropping a backpack and walking away before the second bomb exploded.

‘‘It does seem to be pretty clear that this suspect took the backpack off, put it down, did not react when the first explosion went off and then moved away from the backpack in time for the second explosion,’’ Patrick said. ‘‘It’s pretty clear about his involvement and pretty chilling, frankly.’’

Many questions still remain in the investigation, including whether the FBI paid sufficient attention to Tamerlan Tsarnaev in 2011 after the agency was alerted by Russian authorities that he might have been under the sway of militant Islamic radicals.

“He was on the radar, then he got off the radar,” said Representative Michael McCaul, Chairman of the House Homeland Security Committee and a Republican of Texas.

McCaul said 26-year-old Tamerlan’s six-month trip last year to Russia, where officials have speculated he may have been trained or influenced by terrorist groups in the restive provinces of Dagestan or neighboring Chechnya, looms very large in the ongoing probe.

“That six and half months becomes exceedingly important,” he said. “I would assume the Russians have some intelligence on this individual.”

Others werecritical of the FBI’s handling of the case, including Sen. Lindsey Graham, a Republican of South carolina, who said he believes the FBI may have “dropped the ball.”

“Once you’re brought to attention by a foreign government, I think you should have a red flag put then, to be taken off later,” Graham said on CNN. “The ball was dropped in one of two ways — the FBI missed a lot of things, [or] there’s one potential answer [that] our laws do not allow to follow up in a sound solid way. There was a lot to be learned from this guy. He was on websites talking about killing Americans. He went overseas ... he was clearly talking about radical ideas. He was visiting radical areas.”

“The fact that we could not track him has to be fixed,” Graham added. “It’s people like this that you don’t want to let out of your sight, and this was a mistake. I don’t know if our laws are insufficient or the FBI failed, but we’re at war with radical Islamists and we need to up our game.”

Menino said it has become clear that the older brother, Tamerlan, was the more influential, describing him the “leader” and the 19-year-old Dzhokhar as a “follower.”

“His [older] brother read those magazines that are published on how to create bombs…,” Menino said.

Menino defended the decision to ask Boston residents to remain in their homes and not venture onto streets on Friday, because of the potential threat of more violence and the ongoing manhunt for Dzhokhar.

“I had information that there was other things going on during the [time the] decision that was made,” he said. “At that time, we found a pipe bomb in another location in our city of Boston, another individual was taken into custody in another location.’’ He did not elaborate on the discovery of the other pipe bomb.

Patrick said separately on NBC’s “Meet the Press” that he didn’t know when the younger Tsarnaev might be able to speak to authorities, but that investigators were ready to question him as soon as he could be interviewed.

“There are lots of questions about how and why,” Patrick added on CBS.

Whether Dzhokhar Tsarnaev will face the death penalty if convicted was another topic discussed Sunday. Senator William “Mo” Cowan, appearing on CNN’s State of the Union, and Patrick said they would leave that decision to the Department of Justice.

Menino was asked if he would favor prosecution of Tsarnaev in federal court and whether he expected Tsarnaev to face the death penalty.

“I hope that the U.S. attorney, Carmen Ortiz, takes him on the federal side and throws the book at him,” Menino said.