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A Turkish security official on Tuesday said two of the Moscow concert hall attack suspects travelled "freely" to Russia as no arrest warrants were issued against them.

Russian authorities detained 11 people in connection with Friday's attack, which saw camouflaged gunmen storm into Crocus City Hall, open fire on concert-goers and set the building ablaze, killing at least 139 people.

Two of those, Tajik nationals Rachabalizoda Saidakrami and Shamsidin Fariduni, "were able to travel freely between Russia and Turkey since there was no warrant for their arrest", the official told AFP, speaking on condition of anonymity.

The two had both spent time in Turkey shortly before the attack and entered Russia together on the same flight from Istanbul, the official said.

The Islamic State group has said it was responsible for the Moscow attack, and IS-affiliated media channels have published graphic videos of the gunmen inside the venue.

Russian President Vladimir Putin on Monday acknowledged for the first time that "radical Islamists" were behind last week's attack at the concert hall, but suggested they were linked to Ukraine.

Turkish authorities, meanwhile, have rounded up scores of suspects with alleged links to IS extremists in nationwide raids, a government minister said on Tuesday.

During simultaneous raids carried out in 30 cities across the country, 147 suspects were detained, Interior Minister Ali Yerlikaya announced on social media.

'Radicalised in Russia'

Turkish authorities established that one suspect, Fariduni, entered Turkey on 20 February and returned to Russia via Istanbul airport on 2 March.

The suspect checked into a hotel in Istanbul's conservative Fatih neighbourhood on 21 February and checked out six days later.

During his initial questioning, he admitted to have travelled to Turkey because his visa in Russia had expired, according to the Turkish official.

Fariduni posted eight times on his social media account on 23 February, with the location set as "Aksaray Istanbul", and the pictures apparently showing the Fatih Mosque, the official said.

The other suspect, Saidakrami, arrived in Istanbul on 5 January. He checked into a hotel in Fatih the same day and checked out on 21 January.

He then returned to Moscow on 2 March on the same flight as Fariduni, according to the Turkish official.

"We assess that both individuals became radicalised in Russia given the short amount of time they spent in Turkey," he told AFP.

The official said Turkey would continue to fight all terror groups including IS, "without interruption".

Turkish President Recep Tayyip Erdogan condemned the deadly Moscow attack in a phone call with Putin last weekend, with whom he has forged close ties.

Erdogan told Putin Turkey was ready to cooperate with Moscow in the fight against terror, according to his office.