The cousins met several times during Tsarnaev's stay in Dagestan. Kartashov's lawyer, Patimat Abdullaeva, told ABC News by phone that the two did discuss religion, but she insisted Tsarnaev was the one with extremist views. Kartashov is in prison for an unrelated matter -- waving an Islamist flag during a wedding procession -- but his lawyer says Russian investigators have interviewed him there about his interactions with Tsarnaev.
Magomed Magomedov, another member of Union for the Just, told ABC News he also saw Tsarnaev several times last year, at the mosque and around Makhachkala, but could not remember their discussions about religion. He described Tsarnaev as being aloof and out of place in Dagestan.
"He was sticking out, it was obvious he is not local. He liked to draw attention with his expensive and fancy clothes. His haircut was something no one has seen before," he said.
That description matches the picture that investigators are painting of Tsarnaev. They said when Tsarnaev arrived in Dagestan, his flashy appearance and demeanor immediately set him apart.
He also apparently drew attention to himself by claiming to know more about Islam than he really did. According to investigators, Tsarnaev would often recite things he had read or seen on the internet, often confusing those he was trying to impress.
"He was driving people crazy," one official said.
The officials said he was not as strict a practitioner of Islam as he claimed to be.
While his younger brother and alleged co-conspirator Dzhokhar has been described as the family pothead, one official said Tamerlan was also fond of marijuana, spending hours high on the couch in Massachusetts where he did not have a steady job.
The FBI has met with Tsarnaev's parents at least once. Officials said they are still planning to meet with nine or 10 other individuals, including with Tsarnaev's extended family, childhood friends, and contacts at the mosque. Those meetings were described as "tying up loose ends" rather than suspicious leads.
Amid Tensions, U.S.-Russia Play Nice on Boston Investigation
The American officials praised the unusual level of cooperation they've received from their Russian counterparts.
Often that relationship is plagued by lingering Cold War-era mistrust, but officials described how both sides have poured over linkage maps together, with the Russians sharing their knowledge and analysis, even suggesting individuals that the American side may want to interview. That, they say, is different from the past when the Russians offered little more than terse responses to American requests for information.
Indeed, that mistrust may have hindered early attempts to investigate Tsarnaev in 2011, when Russia asked the United States to look into what it suspected were Tsarnaev's plans to join extremist groups abroad. The FBI found nothing to support those claims, but said Russia did not follow up when the bureau asked for more information. That communication gap has become a target for a group of American lawmakers who plan to visit Russia next week to investigate the bombing.
"If there was a distrust, or lack of cooperation because of that distrust, between the Russian intelligence and the FBI, then that needs to be fixed and we will be talking about that," Rep. Dana Rohrabacher (R-Calif.), the chairman of the House Committee on Foreign Affairs' Subcommittee on Europe, Eurasia and Emerging Threats who is leading the Congressional delegation, told ABC News by telephone.
While the officials described their cooperation with the Russians as "unprecedented," they grumbled privately that they have been unable to do a methodical step-by-step investigation like they are used to doing in the U.S., or even in other countries where they have long-standing cooperation. American investigators from the FBI have been unable to travel to Dagestan without permission from the Russian authorities.
Still, they insist they have been able to confirm much of what they have been told by Russian government officials from what one official vaguely described as "other channels."
ABC News' Dada Jovanovic contributed to this report.