The man accused of the Boston marathon bombings justified the killings of innocents in a blood-stained message he scrawled on the inside of a boat, his trial has heard.

Jurors were shown the note, written in pencil and pocked with bullet holes, in the city's US District Court on Tuesday.

Prosecutors say Dzhokhar Tsarnaev hid in the boat in the yard of a home in suburban Boston, during the manhunt for the bombers two years ago.

The message read: "The US Government is killing our innocent civilians but most of you already know that.

"As a M (bullet hole) I can't stand to see such evil go unpunished, we Muslims are one body, you hurt one you hurt us all.

"Now I don't like killing innocent people it is forbidden in Islam but due to said (bullet hole) it is allowed."

He also wrote that he was jealous of his older brother, Tamerlan Tsarnaev, because he was dead and in paradise, the court heard.

The accused inadvertently ran over and killed his 26-year-old brother with a car days after the bombing as he fled a gunbattle with police, the trial has heard.

Earlier on Tuesday, the court was told Tsarnaev attended the Boston marathon the year before the attack, posting a cryptic tweet that day.

FBI agent Stephen Kimball said Tsarnaev, using the Twitter handle J_Tsar, wrote: "They will spend their money and they will regret it and then they will be defeated".

FBI agents also testified that some of the 3,000 pieces of evidence, including shrapnel and body parts, retrieved from the blast sites were found on rooftops four storeys up.

On Monday, the trial saw a video which prosecutors said showed the Tsarnaev brothers at the scene of the marathon explosions.

Tsarnaev is accused of killing three people and injuring 264 with a pair of homemade bombs at the race's crowded finish line on 15 April 2013.

He is also charged with the fatal shooting of a police officer three days later.