Kenyan security forces remained locked in a tense stand-off with armed terrorists in a Nairobi shopping centre today as the death toll continued to rise.

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.

Joseph Lenku, the interior Cabinet secretary, said Kenyan forces had control of the security cameras inside the mall and military troops and police had surrounded the building.

Kenyan president Uhuru 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.

Foreign Secretary William Hague said Britons had undoubtedly been caught up in the "callous and cowardly and brutal" assault by a heavily-armed gang who singled out non-Muslims.

Mr Hague said "we should be ready for that and aware of that" as he revealed that the Government's emergency response committee Cobra had met and a rapid deployment team was being sent to Kenya to help.

Two Canadians, including one diplomat, and two French women have been confirmed as among the dead.

The US State Department also said four American citizens were reported injured.

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.

And he 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, Daniel Howden, reporter for The Independent, 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.

Nairobi's mortuary superintendent, Sammy Nyongesa Jacob, said Africans, Asians and Caucasians were among the bodies brought in following the attack.

Speaking from his country residence Chevening, in Kent, Mr Hague said there had been a claim of responsibility from al-Shabaab but "that doesn't mean we know for certain who has done or is doing this.

"I think what we do know for certain and what we can say in the United Kingdom for certain is that all of our work and the work of Kenya and other countries neighbouring Somalia to bring stability to Somalia, to defeat terrorism there, will continue.

"It will never be deterred or prevented by actions of this kind. I know that will be the view of the Kenyan government and the people of Kenya as well."

He said al-Shabaab had brought "terror and great difficulty to Somalia" and the UK had done a lot of work to tackle the problems in Somalia.

"It is too early to know for sure who carried out this attack. It is an attack that, as we speak, as far as we know is still continuing so we can't give any further details."

He added: "These are large numbers of entirely innocent people, that's why I say it is a particularly callous and cowardly and brutal attack.

"Sadly significant numbers have been killed. So again I say that the thoughts of the UK are with the people of Kenya at this terrible moment."

The Foreign Secretary 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.

"We are sending a rapid deployment team to reinforce that work, which will be particularly important if the situation carries on. We have offered the Kenyan authorities any other assistance and of course we will keep in touch with them about that."

A Downing Street spokesman said David Cameron had spoken to Mr Kenyatta and passed on his "sincere condolences".

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".