(CNN) -- Investigators are searching a New Bedford, Massachusetts, landfill for Boston Marathon bombing suspect Dzhokhar Tsarnaev's laptop and other clues into the April 15 attack, a law enforcement official with knowledge of the investigation told CNN's Susan Candiotti on Friday.
The source said Tsarnaev himself, as well as clues from other sources, led them to the dump near the University of Massachusetts-Dartmouth, where Tsarnaev attended classes.
Tsarnaev has not given investigators any substantive information since officials informed him of his constitutional rights prior to charging him with use of and conspiracy to use a weapon of mass destruction, the source said Friday.
But the the source described the earlier bedside questioning as "very thorough" and said investigators do not feel hamstrung.
Meanwhile, Tsarnaev has been moved from a Boston medical center to a federal Bureau of Prisons hospital about 40 miles away.
Dzhokhar Tsarnaev had been receiving treatment for a variety of wounds at Beth Israel Deaconess Medical Center since his capture nearly a week ago.
He is now at Federal Medical Center Devens, U.S. Marshals Service spokesman Drew Wade said Friday.
The prison hospital, located on the grounds of the former Fort Devens military base, is designed to house prisoners requiring ongoing medical care, according to the facility's website.
Tsarnaev, 19, was captured April 19 after a nearly 24-hour manhunt. According to the criminal complaint accusing him in the bombing, he had what appeared to be gunshot wounds to his head, neck, legs and hand. His brother, Tamerlan, died after a gun battle with police last week.
Authorities say the Tsarnaevs were responsible for twin blasts on April 15 that killed three people and injured more than 260, 14 of whom had limbs amputated.
Some of the wounded were treated at Beth Israel Deaconess, and were upset that the suspect in the bombing also was being treated there, a doctor with colleagues at the hospital told CNN's Elizabeth Cohen. Some felt anxiety and fear knowing the suspect in the bombing was in the building, the doctor said.
As of Thursday evening, 34 of the wounded were still being treated at Boston hospitals, including one patient in critical condition.
A law enforcement official told CNN Thursday that at least one of the two bombs, the second to explode, was detonated by remote control.
Spontaneous plan to attack New York City
On Thursday, officials revealed that New York City was the next target for the Boston Marathon bombing suspects. It was a spontaneous idea, Tsarnaev told investigators from his hospital bed.
But a botched carjacking spoiled the impromptu road trip to Times Square, Tsarnaev said. They still had six improvised bombs at the time.
"We don't know that we would have been able to stop the terrorists had they arrived here from Boston," Mayor Michael Bloomberg said. "We're just thankful that we didn't have to find out that answer."
Before forcing their way into the vehicle the night of April 18, the brothers shot dead a campus police officer at the Massachusetts Institute of Technology, police said.
The hijacked vehicle, a Mercedes SUV, ran low on fuel and they stopped at a service station, where the vehicle's owner escaped. Shortly thereafter, police picked up the trail of the SUV. A pursuit followed, during which, authorities say, the men were throwing the bombs out the vehicle's window at them. The gun battle and Tamerlan Tsarnaev's death followed.
A previous trip
There is no evidence that New York City remains a target of a terror attack stemming from the Boston bombings, New York City Police Commissioner Ray Kelly said. Still, he said authorities are investigating two visits that the surviving suspect made to New York City last year.
In one of those trips, in April 2012, Dzhokhar Tsarnaev was photographed in Times Square. Another person pictured in that photo has been in federal custody for seven days on alleged visa violations.
Federal agents detained that man and another person after swarming Dzhokhar Tsarnaev's University of Massachusetts-Dartmouth residence hall during the search for him on April 19.
The two are foreign exchange students from Kazakhstan enrolled at the Dartmouth campus. Neither has been linked to the attack, but investigators hope they can better piece together the suspects' movements before and after the marathon.
"These guys are not being cut loose immediately, and there's a reason why," the federal law enforcement source said.
Father's visit delayed
Meanwhile the Tsarnaev brothers' parents have left their home in Dagestan for another part of Russia, their mother, Zubeidat Tsarnaev, told CNN Friday.
She said the suspects' father, Anzor Tsarnaev, is delaying his planned trip to the United States indefinitely.
She told CNN's Nick Paton Walsh that her husband was delaying the trip for health reasons. She wouldn't elaborate.
Anzor Tsarnaev had earlier agreed to fly to the United States after FBI agents and Russian officials spoke with them for hours this week at the family's home.
The mother also will not be flying to the United States, where she is wanted on felony charges of shoplifting and destruction of property.
The family lived in Massachusetts before Zubeidat Tsarnaev jumped bail after her arrest on the charges in 2012. The parents moved to Dagestan that year.
Sources: Russia raised concerns about mother, son
Zubeidat and Tamerlan Tsarnaev had previously fallen under the suspicion of Russian authorities concerned they were following radical ideologies.
Russian authorities had raised concerns to U.S. authorities about her and her son, sources told CNN. But a U.S. official said that the Russian's case at the time was "thin."
Zubeidat Tsarnaev said the FBI had visited her family "several times" in 2011 with questions about her older son's "Islamic interests."
U.S. authorities did add Zubeidat Tsarnaev and her older son to the Terrorist Identities Datamart Environment, or TIDE, database in 2011 -- a collection of more than a half million names maintained by the National Counterterrorism Center, an intelligence official said.
Zubeidat Tsarnaev told CNN on Thursday that she didn't want to accept the reality of the bombing, saying it was fake. She has seen a video pushing the wild idea, she said, adding that there was no blood and that paint was used instead.
Nonetheless, she broke down when she spoke of the victims.
"I really feel sorry for all of them. Really feel sorry for all of them," she said, her voice cracking even as she remained resolute that her sons were not involved.
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.
Putin: 'We were right'
Russian President Vladimir Putin on Thursday urged closer cooperation between other countries' security services in the wake of the Boston attack.
"If we combine our efforts, we will not suffer blows like that," he said during a live televised call-in session in Moscow on Thursday.
In his first on-camera comments since the bombing, Putin also lashed out against those in the West who have slammed Russia for human rights abuses in its actions toward Chechnya.
"Russia is among the first victims, and I hate it when our Western partners call our terrorists -- who committed some heinous crimes in Russia -- when they call them freedom fighters and never call them terrorists. They supported them," said Putin, accusing unnamed people or groups of providing Russia's foes with political, financial and "media" support.
U.S. authorities have come under fire at home, with lawmakers asking if the FBI and CIA failed to share information. Sources told CNN that Russia had separately asked the FBI and the CIA to look into Tamerlan Tsarnaev in 2011.
CNN's Drew Griffin, Dave Alsup, Carol Cratty, Nick Paton Walsh, Brian Todd, Barbara Starr, and Ben Brumfield contributed to this report.