(CNN) -- His older son's body remains unclaimed. His younger son is hospitalized with severe injuries, and faces terrorism and murder charges.
Anzor Tsarnaev is expected to step off a flight in the United States in the coming days after his travel from Dagestan.
He may be bringing along important information for the investigation into the marathon bombings that killed three and injured hundreds on April 15.
He is to depart for the United States as soon as Friday, human rights activist Kheda Saratova told CNN. Saratova is serving as the parents' representative.
Tsarnaev has said he will cooperate in the investigations into the alleged crimes of his sons, Dzhokhar, 19, and Tamerlan, 26. The elder son was killed while the two allegedly violently resisted and fled police.
Though they have relatives living in the United States, no one had claimed Tamerlan Tsarnaev's body as of Wednesday, the Massachusetts chief medical examiner's office said.
Relatives living in the area have publicly remarked that they are ashamed of the two young men. Several Boston-area imams have said they would feel uncomfortable presiding over his funeral.
Russian state media reported that Anzor Tsarnaev's wife, Zubeidat, was supposed to travel with him, but she is wanted on 2012 felony charges of shop lifting and property damage in Massachusetts, according to court officials.
The family lived there before she jumped bail and they moved the same year to Dagestan, a semiautonomous region of Russia, officials said.
Saratova said the suspects' mother would not be traveling to the United States, where there's been an arrest warrant for her since October, according to the Natick District Court.
Characterized in fair condition at a Boston hospital, Dzhokhar Tsarnaev has been communicating with authorities. His father has spoken for hours with U.S. and Russian authorities, Saratova said.
On Wednesday, FBI agents were in Makhachkala, Dagestan -- a city that Tamerlan Tsarnaev called home for several months in 2012 -- to talk with the suspects' parents.
The conversation -- which included members of Russia's federal security service -- ended Wednesday evening, the suspects' mother told Saratova.
Both parents have publicly stated that they believe their children are innocent and were framed -- "just because they were Muslim," as Zubeidat Tsarnaev put it.
When asked whether she thinks her younger son will get a fair trial, she replied, "Only Allah will know."
Russia warned U.S.
The Tsarnaevs are originally from the embattled Russian republic of Chechnya but fled from the brutal wars there in the 1990s. The two brothers were born in Kyrgyzstan and moved at different times to the United States.
The family's adopted republic has become a focus for investigators, especially given that Tamerlan Tsarnaev went there during a six-month trip to Russia last year.
Officials have been looking into what he may have done there during that time. The young man is believed to have posted videos online tied to militant jihadists in the region.
On two occasions before that -- in March and late September 2011 -- Russian authorities asked U.S authorities to investigate Tamerlan Tsarnaev.
A senior U.S. official with direct knowledge of information from the Russians said that the case then "was extremely thin," adding that the European country wanted Tamerlan Tsarnaev questioned to see if he and others had become "radicalized."
NYC 'party' celebration
The brothers may have planned to celebrate the Boston Marathon bombings by driving to New York City and "party," according to Ray Kelly, the New York police commissioner.
Kelly said information collected from the surviving suspect included "something about a party or having a party."
"It may have been words to the effect of coming 'to party' in New York," Kelly said.
A man who was carjacked and held hostage -- allegedly by the two brothers -- just outside Boston last week said he thought he heard the two men say "Manhattan" in their conversation, which was in a language other than English, the commissioner said.
The brothers used a remote control device similar to those used to guide toy cars to detonate the two bombs in Boston, said Rep. Dutch Ruppersberger, a Maryland Democrat and member of the House Select Committee on Intelligence.
The surviving suspect, Dzhokhar Tsarnaev, has indicated that his older brother planned the attack and described him and his brother as self-radicalized jihadists, according to a U.S. government source.
He has denied any direct influence by terror organizations such as al Qaeda.
The teenager cited the U.S. wars in Afghanistan and Iraq as motivating factors behind the attack, a U.S. government official said.
Dzhokhar Tsarnaev has been charged with using and conspiring to use a weapon of mass destruction resulting in death and one count of malicious destruction of property by means of an explosive device resulting in death.
Investigators are looking into the possibility Tamerlan Tsarnaev may have helped finance the bomb plot through drug sales, according to a source familiar with the investigation. He was married with a young daughter whom he frequently cared for while his wife worked as a home health aide.
Boston bouncing back
For more than a week, a stretch of Boylston Street-- traditionally one of the busiest parts of Boston -- had been a crime scene in the aftermath of the blasts that left three dead.
On Wednesday, workers replaced missing bricks and patched up concrete on the street just before opening it to pedestrian traffic. Crews were repairing damage caused by the two bombs, which were placed near the marathon's finish line.
"I think that Boston is a tough city and it will be rejuvenated and ready to go," said David Sapers, owner of Sugar Heaven on Boylston Street.
Those wounded in the explosions, meanwhile, continued to recover as well.
Of the more than 260 people who were hurt, 33 remain hospitalized Wednesday night, according to a CNN tally. One person is in critical condition at Boston Medical Center.
In Cambridge, mourners gathered at the Massachusetts Institute of Technology campus to honor Campus Officer Sean Collier, the fourth person killed last week.
Authorities believe the Tsarnaev brothers shot Collier as he sat in his patrol car Thursday night.
CNN's Michael Pearson, Jake Tapper, Pam Benson, Julia Talanova, Carol Cratty, Brian Vitagliano, Laura Ly, Deborah Feyerick, Nick Paton Walsh, Julian Cummings, Barbara Starr, Susan Candiotti, Jessica Yellin and Joe Johns contributed to this report.