Anzor Tsarnaev and Zubeidat Tsarnaeva agreed to make the trip during a meeting in the Russian republic of Dagestan with a team from the U.S. embassy in Moscow, RIA Novosti reported.
Tsarnaev, the father of Tamerlan and Dzhokhar Tsarnaev, had earlier said he would travel to the United States "as soon as possible."
Tsarnaeva, who arrived in Dagestan Tuesday evening, has said she does not believe her sons carried out the attack.
An uncle of the brothers who lives in Maryland, Ruslan Tsarni, said he believes Tamerlan Tsarnaev, 26, who died in a shootout with police, was "brainwashed" by an Armenian friend in Cambridge, Mass., CNN reported.
"This person just took his brain," Tsarni said.
The uncle said he became so concerned he called a family friend in Cambridge to ask him to look into the friend.
Tsarni did not name the person he felt had influenced his nephew.
Sen. Jim Risch, R-Idaho, a member of the Senate Committee on Intelligence, said the FBI found no "red flags" when they questioned Tamerlan in 2011 and defended the FBI's investigation conducted at the request of the Russian government, The Hill reported.
"I started as a prosecuting attorney, and I know shoddy work when I see it," Risch said. "This was not shoddy work."
He said information supplied to the FBI by Russian intelligence was "much more conclusory than helpful."
Dzhokhar Tsarnaev, 19, the surviving brother, told investigators he and his brother decided just a week or so before the marathon to bomb the event, a law enforcement source told Newsday.
As the investigation continued, traffic began moving Wednesday on Boylston Street, for the first time since two bombs at the marathon's finish line, killing three people and injuring more than 260.
The Boston Globe reported nearly all the debris from last week's carnage had been removed.
A sign in one store window, thanking authorities and mourning the victims, read: "We all stand as one, and we will run again. We are all Boston. Thank you, from the bottom of our hearts. We will reopen soon."
Swim Week Miami Beach 2014 [PHOTOS]