FBI Director Robert Mueller testifies before the Senate Appropriations Committee's Commerce, Justice, Science, and Related Agencies Subcommittee on Thursday. (Chip Somodevilla/GETTY IMAGES)

FBI Director Robert S. Mueller III on Thursday defended the bureau’s handling of a Russian warning about a suspect in the Boston Marathon bombing in the months before the attack.

Mueller told a Senate subcommittee that an FBI investigation of Tamerlan Tsarnaev initiated in March 2011 after a tip from Russian authorities found that Tsarnaev posed no terrorist threat. He said two later attempts to obtain more information from the Russians got no response, and the case was closed.

“As a result of this, I would say, thorough investigation, based on the leads we got from the Russians, we found no ties to terrorism,” Mueller told the Senate Appropriations Committee’s subcommittee on commerce, justice and science.

He acknowledged, however, that electronic notifications that Tsarnaev had left the United States in January 2012 and spent six months in Russia were not shared fully within the Joint Terrorism Task Force in Boston.

“To the extent that we go back and look and scrub and see what we could have done better, this is an area where we’re looking at and scrubbing it and doing better,” the FBI director said.

Tsarnaev, 26, was killed in a shootout with police four days after the April 15 bombing. His brother, Dzhokhar, 19, is recovering from gunshot wounds in a federal prison hospital and faces charges that could carry the death penalty in connection with the bombing, which killed three people and injured more than 260 others. The brothers also are suspected of killing a campus police officer at the Massachusetts Institute of Technology.

Dzhokhar was interviewed by FBI agents before he was charged and told them that he and his brother were motivated out of anger at the U.S. wars in Afghanistan and Iraq. In a new development, a U.S. law enforcement official confirmed Thursday that authorities found a note written on the interior wall of the boat cabin where Dzhokhar was hiding in which he said the bombing was retribution for the wars and called the Boston victims “collateral damage.”

Dzhokhar wrote that he did not mourn his older brother because he was a martyr and that he expected to join him in paradise soon, according to CBS News, which first reported the existence of the message. The official, who spoke on the condition of anonymity to discuss an ongoing investigation, said the writing could be used as evidence against Dzhokhar.

Questions have been raised about whether the FBI should have responded more aggressively to the Russian information on Tamerlan Tsarnaev and about whether the tip was shared properly among law enforcement agencies.

Mueller offered little new information about the FBI’s actions before the bombing or the continuing investigation. He said efforts remain underway to discover whether anyone else was associated with the attack.

The Tsarnaev family was originally from Chechnya, a Russian region where Islamic militants have been waging a battle against Moscow. The family had lived in the Boston area for a decade, but Mueller said Russian authorities reported in March 2011 that they were concerned that Tamerlan planned to return to Russia and join Islamic militants.

In response, Mueller said, an FBI agent in Boston looked into Tsarnaev’s background. He visited the community college Tsarnaev attended and interviewed his parents and then Tsarnaev. Mueller said that the agent found no ties to terrorism and that the bureau got no response when it asked the Russians for any additional information in September and October of 2011. So the case was closed.

Still, Tsarnaev’s name was added to a low-level watch list that notified U.S. law enforcement when he traveled. In January 2012, an automatic notification was sent to a Customs and Border Protection agent with the Boston terrorism task force that Tsarnaev had left the country for Russia. A second notice was sent when he returned six months later.

There have been reports that Tsarnaev met with Islamic militants in Russia. But Mueller said the CBP agent took no action in response to the notices, probably because the office receives hundreds of similar notifications each year.

He said changes in the system will ensure that more attention is paid to such notices.