WASHINGTON (CNN) -- The Senate Intelligence Committee will examine the FBI's handling of Boston Marathon bombing suspect Tamerlan Tsarnaev, chairwoman Sen. Dianne Feinstein told CNN on Monday.
A hearing with FBI officials, expected to take place behind closed doors, could happen as soon as Tuesday, said Feinstein, D-California.
Tsarnaev was questioned by the FBI at the request of Russia before he traveled there last year. Some members of Congress have asked why he wasn't further questioned or monitored by the FBI when he returned to the United States six months later.
He died after a shootout with police on Thursday night. His younger brother and alleged bombing accomplice, Dzhokhar, was captured the next day.
"I have asked the staff director of Intelligence this morning to set a hearing, particularly with FBI intelligence," Feinstein said, adding she hoped for answers about what Tsarnaev did during the trip.
"And when he came back to this country, why didn't it ring a bell with the FBI intelligence unit that he should be checked out and vetted again?" she asked.
Feinstein noted that the U.S. Department of Homeland Security later denied Tsarnaev's application for citizenship, raising another question about who knew what about him.
The purpose of the hearing was "not to criticize, because I am a big fan of the FBI's, but to go back and see that we plug loopholes," Feinstein said.
Before Tsarnaev's 2012 trip, Russian authorities tipped off the FBI that he may be becoming radicalized. The FBI said it interviewed him and found no links to terrorism.
Tsarnaev, who's ethnically Chechen but came to the United States from Kyrgyzstan, spend six months in Russia, causing some legislators and analysts to speculate he may have received training during the trip.
Conservative Sen. Lindsey Graham, who said Sunday the FBI may have dropped the ball in its investigation of Tsarnaev, began easing off that claim on Monday.
In an interview with CNN, the South Carolina Republican confirmed he talked to the assistant director of the FBI and learned that the bureau interviewed Tsarnaev, his parents and classmates.
"They put his name through the system and they sent back this information to the Russians and said, 'Do you have anything else?' And they never got a reply back," Graham said.
On another matter, Graham said Tsarnaev wasn't flagged upon leaving for Russia or returning because of an apparent misspelling of his name by the Russian airline Aeroflot.
"It didn't get into the system because of a misspelling," Graham said. "Now whether or not he intentionally changed his name or Aeroflot just got the spelling wrong, I don't know. That's to be determined."
As for apparent warning signs that occurred within the last year, such as YouTube postings of radical Islamists, Graham said the FBI told him "they have limitations on what they can do."
"So maybe it's the system failed, didn't provide the FBI with the tools, or maybe they didn't use it properly," he added. "That's why maybe we need to find out what happened."
His comments sounded similar to those made by House Intelligence Committee Chairman Mike Rogers, who defended the FBI on Sunday.
He told NBC the agency "did their due diligence" but Russian authorities "stopped cooperating" when the United States sought further clarification.
Rogers also said he believed Tsarnaev may have traveled overseas on an alias.
Graham said Monday that the country needs to revisit its laws for how it investigates extremism on U.S. soil.
"I don't want a police state, but I want a nation where the police can protect us," he told Fox News.
CNN's Ashley Killough contributed to this report.