Speculation, accusations and denials swirled Sunday as officials looked into a possible connection between the alleged Boston Marathon bombers and extremist elements in their homeland.

Dagestan and area

Republican lawmakers in Washington said they suspected Dzhokhar and Tamerlan Tsarnaev were part of a larger conspiracy — perhaps linked to Islamic extremists in the southern Russian republics of Dagestan and Chechnya — while some of those same extremists and officials in Boston made separate suggestions that the marathon bombing was a "lone wolf" attack.

Both of the predominantly Muslim republics have militant separatist movements. The Tsarnaev family reportedly has roots in both territories and in nearby Kyrgyzstan, though the brothers had been living in the U.S. for years.

The elder brother, 26-year-old Tamerlan, who died Friday following a wild shootout with police, visited Dagestan in 2012. The six-month trip quickly became a focus of the investigation.

"I personally believe that this man received training when he was over there and he was radicalized," Michael McCaul, a Republican congressman from Texas who also chairs the House Homeland Security Committee, said on CNN's State of the Union. "Clearly something happened, in my judgment, in that six-month time frame — he radicalized at some point in time. Where was that and how did that happen?"

Some friends and family members have said publicly that Tamerlan, who was Muslim, returned from that trip noticeably different, with a much more religious mindset. It has been suggested he turned to radical Islam and led his younger brother down the same route.

Denial from Dagestan

But officials in Boston and the foremost extremist group in Dagestan see things differently.

The mayor of Boston and the chief of police in nearby, suburban Watertown — where Tamerlan was killed, and 19-year-old Dzhokhar was captured over the weekend — both say the evidence points away from a broader conspiracy.

"All of the information I have is they acted alone," Mayor Thomas Menino told ABC's This Week.

Meanwhile, the Dagestan-based Caucasus Emirate distanced itself from the bombing, insisting it has no quarrel with the U.S. and no longer carries out attacks against civilians.

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Caucasus Emirate leader Duko Umarov has prohibited attacks against civilians. (Kavkazcenter.com/Associated Press)

"We are fighting with Russia," the extremist, separatist group said in a statement Sunday, going on to note that its leader — Doku Umarov, the most wanted man in Russia — has ruled-out attacks against civilian targets. The Caucasus Emirate has previously claimed responsibility for a suicide bombing at Moscow's Domodedovo airport in January 2011 that killed 37 people and for suicide bombings on the Moscow subway that killed 40 in 2010. 

But the group stopped short of denying it had any connection to the Tsarnaevs.

It went on to suggest that Moscow was somehow to blame for the attack, but did not offer any details.

Russian security forces appear to consider the bombing an internal matter for the Americans. Media reports there suggest the Tsarnaev brothers had no meaningful connections in the region.

"They were sort of foreigners in their own land," Arne Kislenko, an expert in international relations and security at Ryerson University in Toronto, told CBC News Network on Sunday.

"They have no contacts that seem to be serious enough to link them to known terrorist groups operating in the area."

Kislenko is among those who have suggested an attack by one or more full-fledged militants would probably have been even more devastating than the twin explosions seen on Monday at the Boston Marathon, which killed three and injured 170. 

"Not to be cynical, but [these]

attacks would have been much more deadly and effective if carried out by the likes of a terrorist organization," he said. 

Moscow's suspicions

Moscow had its suspicions about Tamerlan as far back as 2011 and, as was revealed on Friday, asked the FBI to question him on allegations that he was "a follower of radical Islam" and had joined "unspecified underground groups."

The FBI concluded he was not a threat and had no links to militant organizations, and is now facing tough questions about whether it missed something.

But according to Kislenko, the U.S. might not get much help from Moscow in any subsequent investigation.

"This is not a government that’s likely to co-operate too, too much with the United States on that front," he noted. "I wouldn’t count too much on the Russians disclosing much about their operational procedures and what kind of information sources they have." 

Russia may be more concerned with its own security as it prepares for next year’s Olympics in Sochi, which lies in the heart of the restive Caucasus region and has been the site of attacks in the past. 

The Olympics is "number one on the Russian security agenda," said Kislenko, and the events in Boston, whether connected extremists in the Caucasus region or not, are likely to "dramatically increase" those precautions.

With files from Associated Press