An attorney for Boston Marathon bomber Dzhokhar Tsarnaev urged a federal appeals court on Tuesday to toss his client's death sentence due to juror misconduct claims. 

Tsarnaev is making a renewed push to avoid execution after the Supreme Court last year reinstated the death sentence imposed on him for his role in the bombing that killed three people and injured hundreds more near the finish line of the marathon in 2013.

His attorneys are questioning issues that were not considered by the high court, including whether the trial judge had wrongly denied his challenge of two jurors who defense attorneys say lied during jury selection questioning.

One juror said she had not commented about the case online but had retweeted a post calling Tsarnaev a "piece of garbage." 

BOSTON POLICE UNVEILS HOW MANY ICE DETAINER REQUESTS IT IGNORED LAST YEAR UNDER CITY'S SANCTUARY LAW: REPORT

Boston Marathon bomber Dzhokhar Tsarnaev

Dzhokhar Tsarnaev, convicted and sentenced to death for carrying out the Boston Marathon bombing attack on April 15, 2013, that killed three people and injured more than 260, is pictured in this photograph released by the Federal Bureau of Investigation on April 19, 2013. ((FBI via AP, File))

Additionally, defense lawyers said another juror said that none of his Facebook friends had commented on the trial, even though one had urged him to "play the part" so he could get on the jury and send Tsarnaev to "jail where he will be taken of."

They said that while they had tried to raise those concerns during jury selection, the judge chose not to look into them further.

"This case was tried in Boston on a promise... that despite the extraordinary impact of the marathon bombing on this community," a thorough examination of possible jurors would remove anyone unqualified, Tsarnaev attorney Daniel Habib told the 1st U.S. Circuit Court of Appeals judges. "That promise was not kept."

Runners at the finish line of the Boston Marathon

Runners pass the site of 2013's first bombing in front of Marathon Sports at the Boston Marathon finish line ground level on Boylston Street in Boston April 21, 2014.  (Photo by John Tlumacki/The Boston Globe via Getty Images)

However, Justice Department lawyer William Glaser said the trial judge did nothing wrong in his handling of the jurors, though he acknowledged that the jurors made inaccurate statements. 

He said other disclosures they had made to the court suggest that they were just not remembering correctly. 

NASHVILLE CHRISTMAS BOMBING, 2 YEARS LATER: HOW AN EMERGENCY PHONE OUTAGE AMID DISASTER SPURRED CHANGE

"There is no indication in this record that the inaccuracies were the kind of knowing dishonesty that would lead to disqualification," Glaser said.

However, Judge William Kayatta Jr. questioned how the trial judge could know that without looking further into Tsarnaev’s claims. Judge O. Rogeriee Thompson told the Justice Department lawyer she found it difficult to see how Tsarnaev cannot at least plausibly claim that the juror told to "play the part" was knowingly lying.

A running shoe memorial to the victims of the 2013 Boston Marathon bombing

A running shoe memorial to the victims of the 2013 Boston Marathon bombing. The words "Boston Strong" are written on the side of one of the shoes. (Gregory Adams via Getty Images)

At the trial's start, Tsarnaev's lawyers acknowledge that he and his older brother, Tamerlan Tsarnaev, set off the two bombs killing 23-year-old Lingzi Lu, 29-year-old Krystle Campbell and 8-year-old Martin Richard.

They have argued that he should not be put to death, saying his brother – who died in a gunbattle with police – had radicalized him and masterminded the attack.

Tsarnaev was convicted of all 30 charges against him in 2015, including the killing of Massachusetts Institute of Technology Police Officer Sean Collier during the Tsarnaev brothers’ getaway attempt.

People bow their heads during a moment of silence prior to the start of the Boston Marathon

People bow their heads during a moment of silence prior to the start of the Boston Marathon on April 21, 2014, in Hopkington, Massachusetts. (Photo by Andrew Burton/Getty Images)

The 1st Circuit in 2020 overturned Tsarnaev’s death sentence and ordered a new penalty-phase trial to decide whether he should be executed, finding that the judge did not sufficiently question jurors about their exposure to extensive news coverage of the bombing.

CLICK HERE TO GET THE FOX NEWS APP 

The Supreme Court justices, agreeing with the Biden administration, voted 6-3 that the 1st Circuit's ruling was wrong.

The Associated Press contributed to this report.