With the hospitalised Boston bombing suspect unable to speak, attention shifted Sunday to his dead brother, who may have been radicalised or even trained in the Caucasus last year.

US lawmakers questioned why Tamerlan Tsarnaev, killed in a shootout, did not raise more red flags despite being questioned at the request of the Russian government in 2011 and spending six months in the volatile region last year.

"Clearly something happened in my judgment in that six-month timeframe... I'm very concerned," House Homeland Security Committee Chairman Michael McCaul told CNN's "State of the Union."

"I personally believe that this man received training when he was over there and he radicalised from 2010 to the present."

Republican Senator Lindsey Graham and Democratic Senator Chuck Schumer also expressed concern about Tamerlan Tsarnaev, who was 26.

"It's people like this that you don't want to let out of your sight, and this was a mistake," Graham said about the oldest of the two brothers, ethnic Chechens who had been living in the United States for a decade.

"I don't know if our laws are insufficient or the FBI failed, but we're at war with radical Islamists and we need to up our game."

Dzhokhar Tsarnaev, 19, was under heavy guard in hospital, reportedly unable to speak because of a throat wound suffered in the violent chase that shut down Boston for most of Friday.

The FBI would only say that he was in "serious condition," while Boston Mayor Thomas Menino told ABC television's "This Week:" "We don't know if we'll ever be able to question the individual."

The Tsarnaev brothers are the main suspects in the double bomb attack on the Boston marathon that took three people's lives and wounded about 180. A policeman was killed and another was seriously wounded in a shootout with the suspects.

Counterterrorism agents trained in interrogating "high-value" detainees were waiting to question Dzhokhar -- who is being treated at the same hospital as many of the marathon bombing victims -- a law enforcement official told AFP.

Officials have invoked a "public safety" legal exception that will allow them to question Tsarnaev without reading him his rights to remain silent and to consult a lawyer.

Graham and fellow Republican Senator John McCain have led calls for the teenager to be declared an "enemy combatant," which would give him the same status as Guantanamo "war on terror" detainees.

But Graham has since nuanced his comments, stressing that Tsarnaev should only be considered an enemy combatant for interrogation purposes, and should receive a civilian trial in federal courts, rather than in a military tribunal like foreign suspects with that designation.

Critics have insisted that because Tsarnaev is a naturalised US citizen and authorities have found no ties between him and terror groups so far, he should be granted a criminal civilian trial.

The Tsarnaev family came to the United States from the former Soviet state of Kyrgyzstan around 2002. Dzhokhar became a US citizen in 2012, while his older brother's application was reportedly held up.

Tamerlan began posting militant Islamist videos on social media sites in recent years, and traveled to Dagestan, which borders Chechnya, in 2012. Both Russian regions host separatist rebel groups.

The brothers' social media pages appeared to express sympathy with the struggle in Chechnya, which has been ravaged by two wars since 1994 between Russia and increasingly Islamist-leaning separatist rebels.

But a website used by rebels in Dagestan denied any link to the Boston bombings, saying it was "not waging any military activities against the United States."

"We are only fighting Russia, which is not only responsible for the occupation of the Caucasus, but also for monstrous crimes against Muslims," the Kavkazcenter.com website said.

US President Barack Obama and Russian President Vladimir Putin have agreed to increase cooperation against global terror in the wake of the attacks.

Dzhokhar was caught Saturday after Dave Henneberry saw blood on a boat he kept in his backyard in the Boston suburb of Watertown. When he lifted the tarp, he saw the wounded teenager curled up inside, police said.

Over the weekend, crowds gathered outside the home of Henneberry -- who has gone into hiding to escape the media blitz -- craning their necks to gaze at his bullet-riddled and blood-smeared 1980s boat.

Fifty-eight of the victims from the bomb attack are still in Boston hospitals, with three in critical condition.