Convicted Boston Marathon bomber Dzhokhar Tsarnaev is seeking a new trial in his case, hoping to overturn his sentence in the April 2013 terrorist attack that resulted in the death of three people and injuries to 264 others.

Tsarnaev, through his lawyers, filed a preliminary motion with the US District Court Monday, claiming that there was lack of evidence in his trial, according to Reuters.

Last April, a jury convicted Tsarnaev of the crime. The following month, members of the jury voted unanimously to send him to death by lethal injection.

"Mr. Tsarnaev files the instant motion while intending to make such a supplemental filing'' by Aug. 17, according to the Boston Globe.

The filing is described by his attorneys as a "placeholder" to comply with the deadline set by Judge George O'Toole Jr. in challenging the verdict.

During his sentencing last June 24, Tsarnaev apologised and admitted that he and his brother, Tamerlan, carried out the attack.

"I am sorry for the lives I have taken, for the suffering that I have caused you, for the damage I have done, irreparable damage," said Tsarnaev.

He added, "In case there is any doubt, I am guilty of this attack, along with my brother," Tsarnaev.

O'Toole told him: "It is tragic ... that you succumbed to their demonic siren song. As long as your name is mentioned, what will be remembered is the evil you've done."

Tsarnaev could use all legal remedies and his case could take years. He could take comfort in the fact that only three of the 74 death-row inmates serving for federal crimes since 1998 have been executed.

The Boston bombing resulted in the deaths of Martin Richard, 8; Chinese exchange student Lingzi Lu, 26; and Krystle Campbell, 29.

The Tsarnaev brothers then killed police office Sean Collier three days later. Tamerlan died in a gunfight with the police and when he was ran over by a car driven by Dzhokhar.

Tsarnaev is currently serving his sentence at a prison in Florence, Colorado.