Mr Hague said the attack at the mall in the capital Nairobi, which has left at least 39 dead and 150 injured, was "callous and cowardly and brutal".
Earlier, the prime minister spoke to Kenya's President Uhuru Kenyatta and offered condolences and assistance.
A rapid deployment team is being sent to Nairobi by the Foreign Office.
The government's emergency response committee, Cobra, has met to discuss the attacks.
And the head of the UK's diplomatic service, Sir Simon Fraser, said the Foreign Office's crisis team in London would be working through Saturday night and would be on standby to give consular assistance to British citizens.
The Somali-based militant group al-Shabaab has said it carried out the attack in which men armed with guns and grenades stormed the Westgate Mall and targeted non-Muslims.
It told the BBC it was in response to Kenyan military operations in Somalia.
Hannah Chisholm, a Briton visiting Nairobi, said she and 60 others barricaded themselves into a large storeroom.
She told the BBC: "We kept running to different places but the shots were getting louder so we barricaded ourselves along with about 60 others into a large storeroom.
"There were children hiding with us as well as someone who had been shot."
She added: "The gunfire was loud and we were scared but at that point we thought the gunmen were thieves so we assumed they wouldn't try to reach the storeroom."
Early on Sunday, the Kenya National Disaster Operation Centre tweeted: "KDF [Kenya Defence Forces] & Special Forces have control of #Westgate 1st and 2nd floors. Parts of the ground floor and basement remain unsecured."
It confirmed hostages were still being held in these unsecured areas.
A Downing Street spokesman said: "President Kenyatta updated the prime minister on the current situation and explained that Kenyan security forces were bringing the situation under control."
He added that the prime minister had passed on his condolences and said the UK government "were ready to provide any assistance we could".
Mr Hague said "the thoughts of the UK are with the people of Kenya at this terrible moment".
In response to al-Shabaab's statements, he said work to "bring stability to Somalia, to defeat terrorism there, will continue".
He added: "Our High Commission staff in Nairobi are working very hard, visiting hospitals, trying to make sure that they are aware of British nationals who might have been in the area or caught up in this."
The minister for Africa, Mark Simmonds, also condemned the attack and offered his "deep sympathy to those affected".
Mr Simmonds said he had spoken to Kenya's foreign minister.
Source: BBC
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