Boston Marathon bombing suspect Dzhokhar Tsarnaev informed investigators that he and his brother were not directed by a foreign terrorist organization. Instead, they were “self-radicalized” and motivated to kill, in part, by U.S. wars in Iraq and Afghanistan, the Washington Post reported.

The 19-year-old also acknowledged his role in the attack while being questioned by investigators in his hospital bed, the report said. Tsarnaev, who has a gunshot wound to the throat and was sedated, responded in writing. He also suffered gunshot wounds in the head, neck, legs and hand during a late-night shootout in Watertown, Mass.

Meanwhile, Tsarnaev's condition is improving, the FBI said on Tuesday. The college student, who had been listed in serious condition at Beth Israel Deaconess Medical Center since his capture on Friday, is now in fair condition, the bureau said.

The update comes a day after Tsarnaev was charged with two federal counts of using a weapon of mass destruction to kill, injure and cause widespread damage at the marathon. Tsarnaev was informed of the charges and read his rights in his hospital room on Monday morning, and placed in the custody the U.S. Marshal Service. If convicted, he could face the death penalty.

[Related: ‘#FreeJahar’: Support for Dzhokhar Tsarnaev seen on Twitter]

Three people were killed and more than 200 others wounded when two powerful homemade bombs exploded near the race’s finish line. Dzhokhar and his 26-year-old brother, Tamerlan Tsarnaev, who was killed by police as the two attempted to avoid capture, are suspected of planting those bombs.

Tamerlan was an ardent reader of jihadist websites and extremist propaganda, U.S. officials told the Associated Press, suggesting the brothers were motivated by an anti-American, radical version of Islam.

Meanwhile, U.S. investigators traveled to southern Russia on Tuesday to speak to the parents of the brothers, a U.S. Embassy official told the news service. Zubeidat Tsarnaeva, the mother of the suspects, and their father, Anzor, are in Dagestan, a predominantly Muslim province in Russia's Caucasus.

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After the bombings, Anzor said he believed the brothers were set up and called Dzhokhar a "true angel." Maret Tsarnaeva, the brothers' aunt, who lives in Toronto, also said she believes her nephews were framed.

Family members are not the only ones expressing doubt.

Many Twitter users have been expressing support for Dzhokhar using the hashtag #freejahar.

And just like the conspiracy theorists who claimed last week that the Boston Marathon attacks were staged, the support for Dzhokhar has been fervent despite his reported confession.

A Change.org petition to "guarantee Dzhokhar Tsarnaev the right to a fair trial," addressed to President Barack Obama, has more than 6,000 supporters.

"We believe that within the chaos caused by the Boston Marathon explosion, two young men were wrongfully accused of something they did not do, and one of them has lost his life before even getting the opportunity of a proper trial," Anita Temisheva, the user who launched the petition, wrote. "We do not wish to see blood of yet another innocent victim, someone who, by U.S. law, is innocent until proven guilty. It is vital to end this persecution, as all the conflicting information shown by the media, and footage from the incident, seen by people from all corners of the world, doesn't manifest itself as enough evidence to condemn Dzhokhar Tsarnaev of this heinous crime."