(CNN) - Sen. Lindsey Graham, who said Sunday the FBI may have dropped the ball in its investigation of Tamerlan Tsarnaev, began easing off that claim Monday, saying instead the agency "responsibly handled" the situation.
The Republican senator from South Carolina said he talked to the assistant director of the FBI after he made his assertions Sunday and had some of his questions answered, including why the case was cleared and how Tsarnaev may have been able to travel to Russia in 2012, a 'misspelling' keeping his name from getting flagged.
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Tsarnaev and his younger brother, Dzhokhar, are the two prime suspects in last week's Boston Marathon bombing. Tsnaraev died following a shootout with police Thursday night, while his younger brother, 19, is hospitalized and in federal custody.
Graham was one of many lawmakers- including Republicans and Democrats-who demanded answers from the FBI on what happened following their investigation of Tsarnaev in 2011. Russian authorities tipped off the FBI that Tsarnaev, who's ethnically Chechan but came to the U.S. from Kyrgyzstan, may be becoming radicalized.
Tsarnaev traveled to Russia for six months in 2012. Some have argued that he was already being radicalized and received further training during that trip.
On CNN's "State of the Union," Graham told Chief Political Correspondent Candy Crowley the FBI either missed "a lot of things" in its investigation, or federal laws did not allow the FBI to "follow up in a sound, solid way."
But on Monday, Graham apparently had some of his questions answered. In an interview with CNN's Jim Acosta, the Republican senator confirmed he talked to the assistant director of the FBI after he made his assertions Sunday. The FBI interviewed Tsarnaev, his parents, and the people he went to school with, Graham said Monday.
"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," he said.
Graham was also fuming Sunday that a red flag wasn't placed on Tsarnaev when he left the country the following a year. But on Monday, he said that was apparently because of a misspelling reported by the Russian airline, Aeroflot.
"It didn't get into the system because of a misspelling," he told CNN. "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."
Democratic Sen. Dianne Feinstein, chairwoman of the Senate Select Committee on Intelligence, told CNN she's calling for a hearing with the FBI to find out when Russia called to ask about Tsarnaev, as well a host of other questions.
"What did he do when he went back for six months? Did he sit in his aunt and uncle's home for six months, or was he doing something else? 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?"
"The (Department of Homeland Security) clearly denied him to be naturalized as a citizen for some reason so I think, not to criticize because I am a big fan of the FBI's, but to go back and see that we plug loopholes is really critical," she added.
White House Press Secretary Jay Carney repeated a statement from the FBI during the daily press briefing Monday, saying the agency "thoroughly investigated" the information it received from Russia in 2011.
In addition to interviews with Tsarnaev and his family members, the FBI says it checked databases, phone conversations, travel history and plans, and associations with persons of interest.
At the time, Carney said, they "did not find any terrorism activity, domestic or foreign."
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, saying on NBC the agency "did their due diligence" but Russian authorities "stopped cooperating" when the U.S. sought further clarification. Rogers also said they 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 said on "Fox and Friends."
The senator reiterated his stance that he wants the younger Tsarnaev to be held as an "enemy combatant," so authorities can question him without a lawyer present for intelligence purposes. That information, he insisted, could not be used against him in court.
"When we're trying to defend ourselves against enemy attacks, you don't give people lawyers," he argued. "Lawyers are for criminal process. We're talking about national security information being gathered here. And you don't have a right to a lawyer there."
But Carney announced Monday he "will not be treated as an enemy combatant."
The hospitalized suspect has "made an initial appearance in the hospital room in front of a federal magistrate judge," Gary Wente, circuit executive for 1st Circuit federal courts, told CNN on Monday.
The federal complaint against Dzhokhar Tsarnaev is under seal, Wente said.
– CNN National Political Correspondent Jim Acosta contributed to this report.