British nationals are "undoubtedly" caught up in the deadly attack on a Nairobi shopping mall and diplomats are trying to obtain full details of any casualties, Foreign Secretary William Hague said on Saturday.

Hague said the government's emergencies committee COBRA had convened to discuss the attack in the Kenyan capital, and a special diplomatic response team had been sent to beef up the consular staff there.

Hague said Britain "unreservedly" condemned the "particularly callous, cowardly and brutal attack", while saying that the claim of responsibility by Somalia's Shebab militant movement had not yet been confirmed.

"There are undoubtedly British nationals caught up in this so we should be ready for that, and aware of that," Hague said in a televised statement following the attack, in which police say 30 people have been killed.

"It is a fast moving situation, it is still going on, we don't have sufficiently precise details to say anything more about that at the moment."

He added that the British High Commission staff "are working very hard on this, trying to identify or account for British nationals who may have been caught up in this."

The United States said earlier that Americans were reportedly among those injured in the violence at Nairobi's Westgate mall.

British Prime Minister David Cameron had spoken to Kenyan President Uhuru Kenyatta and offered him assistance if required, Hague added.

"This is clearly a complex attack, clearly a terrorist attack, and a particularly callous and cowardly and brutal attack targeting innocent people of all ages and so many different backgrounds," Hague said.

"There has been a claim of responsibility by Al-Shebab, that does not mean we know for certain who has done or is doing this," he added.

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