Story highlights FBI director reiterates investigation found no terror ties to Tamerlan Tsarnaev

Source: Dzhokhar Tsarnaev left a message in boat where he was found hiding

He wrote that the Boston Marathon bombing victims were collateral damage

Dzhokhar also said he expected to join his brother in death

Boston Marathon bombing victims were collateral damage in a strike meant as payback for U.S. wars in Muslim lands, the surviving suspect wrote in a message scribbled on the boat where he was found hiding, a law enforcement source told CNN Thursday.

In the message, Dzhokhar Tsarnaev also proclaimed that an attack on one Muslim is an attack on all, and said he would not miss older brother Tamerlan Tsarnaev -- who died after a firefight with police three days after the bombing -- because he would soon be joining him, according to the source.

The writing on the inside of the boat dovetails with what Dzhokhar, 19, told investigators questioning him in a Boston hospital room shortly after his capture, the source said.

CNN has previously cited U.S. officials in reporting that Dzhokhar said U.S. involvement in Afghanistan and Iraq were motivating factors behind the April 15 attack, which killed three people and wounded 275.

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According to authorities, the Tsarnaev brothers fashioned explosive devices from pressure cookers and other materials and detonated them near the finish line of the race.

Three days later, authorities released their images to the public as suspects in the case. Investigators believe they then killed MIT police Officer Sean Collier and hijacked a car before battling authorities in a wild firefight on a Watertown, Massachusetts, street.

Nearly 24 hours later, police found Dzhokhar hiding in the boat after the owner called police to report someone was inside of it.

Dzhokhar -- who suffered gunshot wounds to the head, neck, legs and hands -- is being held a federal Bureau of Prisons medical facility in Devens, Massachusetts. He has been charged with using a weapon of mass destruction and could face the death penalty if convicted.

Tamerlan was secretly buried in a rural Virginia cemetery this month following protests from Massachusetts residents and officials against burying him in that state.

Authorities have said they believe the brothers acted alone, but are investigating whether they could have learned from or been aided by terror groups, including groups overseas.

Of particular interest has been Tamerlan's 2012 trip to the semi-autonomous Russian republic of Dagestan, home to numerous Islamic militant groups that have warred against Moscow's rule.

Russian authorities asked U.S. officials to investigate Tamerlan before the trip, saying they believed he was becoming increasingly involved with radical Islam. The FBI investigated, but found no evidence of extremist activity, FBI Director Robert Mueller reiterated Thursday during a Senate Appropriations Committee hearing.

Mueller said Russian authorities told the FBI that Tamerlan and his mother appeared to be "very religious" and that Tamerlan seemed "intent on returning and perhaps participating in jihad, in Russia."

The FBI conducted a thorough investigation and found "no ties to terrorism," Mueller said.

U.S. officials learned after the bombings that Russian officials had intercepted a 2011 phone call between the suspect's mother, living in Dagestan, and one of her sons, in which they reportedly had a vague conversation about jihad, a law enforcement official told CNN earlier.

Some lawmakers, particularly Republicans, have been critical of how law enforcement, intelligence agencies and the administration of President Barack Obama handled the Russian tip.

While Tamerlan and his mother were added to a terror database following the FBI investigation, Tamerlan was allowed to make his Russian trip in 2012, returning six months later.