Prime Minister David Cameron described the assault on the Westgate shopping centre as an "absolutely sickening and despicable act of appalling brutality".
Mr Cameron said people in the UK should prepare for "further bad news" as the situation developed.
UK staff from Addis Ababa in Ethopia have travelled to assist with the efforts in Nairobi and a rapid deployment team had been sent from London, the Foreign Office said.
Foreign Secretary William Hague has chaired a meeting of the Government's emergency committee Cobra to co-ordinate the response to the situation.
A sombre Mr Cameron said: "It is an absolutely sickening and despicable attack of appalling brutality.
"What we know is that three British nationals have been killed."
He added: "Because the situation is ongoing we should prepare ourselves for further bad news.
"Our thoughts also should be with the Kenyan government and the Kenyan people at this time."
Mr Cameron said he had offered the Kenyan authorities "every assistance" in a call to president Uhuru Kenyatta.
He also indicated that British intelligence assistance could be provided.
Mr Cameron said: "These appalling terrorist attacks that take place, where the perpetrators claim they do it in the name of a religion, they don't.
"They do it in the name of terror, violence and extremism and their warped view of the world.
"They don't represent Islam or Muslims in Britain or anywhere else in the world.
"Obviously the first priority is to make sure we do everything for the British nationals caught up in this, so we're strengthening the consular services that we have and the people that we have to look after our people.
"We've also offered the Kenyans help in terms of policing and advice and intelligence collaboration and other areas which we will be able to help with.
"The situation is ongoing and, as I say that why I think we have to brace ourselves for more bad news as this continues.
"It's an extremely difficult situation but we're doing everything we can to help the Kenyans in their hour of need."
A day after 10 to 15 gunmen - believed to be Islamic extremists - stormed the Westgate Mall attacking shoppers with guns and grenades, an unknown number of hostages remained in the building.
Government officials said at least 59 people were confirmed dead and 175 others were wounded in the atrocity, while about 1,000 were rescued from the upmarket mall.
The Labour Party conference in Brighton paused for a minute's silence as news of the deaths filtered through, with Ed Miliband among those reflecting on the tragedy.
President Kenyatta has pledged to hunt down and punish the terrorists behind the brutal attack in Nairobi.
In a national televised address he said he had "personally lost family members in the Westgate attack".
Somali-based militant group al-Shabaab claimed responsibility for the outrage at the mall in the affluent Westlands district of the capital, which is popular with expats.
The heavily-armed gang singled out non-Muslims as they carried out the attack.
In his speech last night, Mr Kenyatta said security forces were in the process of "neutralising the attackers and securing the mall" but he said it was a "delicate" operation.
He urged Kenyans to "remain calm and vigilant" and asked them to donate blood to help treat the injured. The UK's high commissioner Christian Turner was among those responding to the appeal for blood donors.
President Kenyatta vowed: "We shall hunt down the perpetrators wherever they run to. We shall get to them and we shall punish them for this heinous crime."
Terrified shoppers told of how they huddled in back hallways and prayed they would not be found by the Islamic extremist gunmen.
When the way appeared clear, crying mothers clutching small children and blood-splattered men sprinted out of the four-storey mall.
Witness Elijah Kamau said the gunmen told Muslims to stand up and leave and that non-Muslims would be targeted, as they began their attack.
The gunmen threw grenades and then opened fire, sending shoppers and staff fleeing for their lives.
Speaking from Nairobi, The Independent's Daniel Howden told the BBC that a "massive operation" was still ongoing inside the mall this morning where the gang continued to hold an unknown number of people hostage.
Al-Shabaab, also known as Harakat al-Shabaab al-Mujahideen, earlier tweeted that there will be "no negotiations whatsoever".
The group claimed responsibility for the atrocity, writing on its official Twitter feed that "the Mujahideen entered Westgate Mall" at around noon local time yesterday.
It said it had previously warned the Kenyan government that, if they did not remove military forces from Somalia, there would be "severe consequences".
"For long we have waged war against the Kenyans in our land, now it's time to shift the battleground and take the war to their land," it tweeted.
It added that they were "still inside the mall, fighting the Kenyan kuffar inside their own turf" before the account was suspended by Twitter.
The organisation claimed it had killed more than 100 Kenyan "kuffar", a derogatory term used to describe non-Muslims.
Kenya has seen a rise in terror attacks and threats in recent years, some of which are believed to be in retaliation for a military crackdown on al-Shabaab.
The attacks often involve gunmen armed with automatic weapons and grenades, and their targets include bars, nightclubs and restaurants in various parts of the country.
There was a suspected al-Shabaab attack which left five dead and three injured at a restaurant in the eastern city of Garissa in January, and in August last year one person was killed and six more were left injured in the Eastleigh area of Nairobi on the eve of a visit by Hillary Clinton, then the United States secretary of state.
Last month 18 US embassies and consulates across the Middle East and Africa were closed after a message between al Qaida officials about plans for a major terror attack was intercepted.
The chairwoman of the Commission of the African Union, Dr Nkosazana Dlamini-Zuma, condemned the attack in the "strongest possible terms" and said it underlines "the imperative for renewed and reinvigorated efforts to combat terrorism throughout the continent".
Concerned British nationals are advised to monitor Foreign & Commonwealth Office (FCO) travel advice and to contact 020 7008 0000.
This afternoon, Mr Kenyatta said his nephew and his fiancee were killed in the attack.
"These are young lovely people I personally knew and loved," he said, promising retribution against the terrorists, whose number reportedly include armed women.
"They shall not get away with their despicable and beastly acts.
"Like the cowardly perpetrators now cornered in the building, we will punish the masterminds swiftly and indeed very painfully.
"I call on Kenyans to stand courageous and united. Let us not sacrifice our values and dignity to appease cowards.
"Our victory must be conclusive - let us defeat them with our unity."
He praised Kenyans for their support and donating blood to the injured.
He also applauded the international community for its continued support.
Labour leader Mr Miliband said: "This is an appalling attack which has left three British citizens and many others dead.
"Our thoughts are with the families of the victims and the others caught up in this dreadful atrocity.
"Those who carried out this attack will be condemned across the globe. The cold-blooded killing of innocent women, children and men is as despicable as it is shocking.
"This terrible attack reminds us all of the continuing need for vigilance from our security services and ongoing international cooperation in the battle against terrorism.
"I offer Labour's full support to the Government in the coming days as the Kenyan authorities seek to bring this act of terrorism to an end and bring those responsible to justice."