Gordon Brown tonight vowed a "vigorous response" to attacks in Mumbai which have left at least 80 people dead.

The Prime Minister promised to back the Indian government as it responds to the series of incidents carried out by heavily-armed gunmen.

"These outrageous attacks in Mumbai will be met with a vigorous response," Mr Brown said in a statement.

"I have sent a message to (Indian) Prime Minister (Manmohan) Singh that the UK stands solidly with his government as they respond, and to offer all necessary help.

"Urgent action is under way to offer every possible protection to British citizens in the region."

Another 200 people were injured when gunmen, described by police as "terrorists" opened fire on a crowded Mumbai railway station, luxury hotels and a restaurant popular with tourists.

Johnny Joseph, chief secretary for Maharashtra state in India, of which Mumbai is the capital, said the death toll could rise further.

The gunmen attacked the Chhatrapati Shivaji Terminus station in southern Mumbai and Leopold's restaurant, a Mumbai landmark, along with the Oberoi and Taj Mahal hotels.

There were unconfirmed reports of an explosion near the city's domestic airport.

Eye-witnesses caught up in the chaos said that gunmen were looking for Britons and Americans.

Shivraj Patil, minister for home affairs in India told reporters that two terrorists had been shot and two people arrested.

Indian television reports also claim that the country's anti-terrorism chief, Hemant Karkare has been killed in the attacks.

There were also reports that Westerners had been taken hostage although a senior police officer denied this.

India media organisations were reporting that they had received emails from an unknown group, the Deccan Mujahideen, claiming responsibility for the attacks.

Conservative MEP Sajjad Karim was barricaded in a basement room after he fled from machine-gun fire in the Taj Mahal hotel.

He said: "I was in the lobby of the hotel when gunmen came in and people started running. There were about 25 or 30 of us.

"Some of us split one way and some another. A gunman just stood there spraying bullets around, right next to me. I managed to turn away and I ran into the hotel kitchen and then we were shunted into a restaurant in the basement.

"We are now in the dark in this room and we've barricaded all the doors. It's really bad."

He said that as he ran from the lobby, he saw people falling but did not know the extent of any casualties. He said it seemed to be a "random attack".

North West MEP Mr Karim is part of a trade delegation visiting Mumbai for talks but all the other members of the group, which included two British MEPs are now thought to be safe.

Alex Chamberlain, who works for a sports website and was in the city on business, told Sky News the gunmen burst into the Oberoi hotel's restaurant and herded diners upstairs.

He said he believed they were looking for British and American visitors.

"They told everybody to stop and put their hands up and asked if there were any British or Americans. My friend said to me 'don't be a hero, don't say you are British'.

"I am sure that is what this is all about. They were talking about British and Americans specifically."

He said that he and another man managed to escape the gunmen through a fire exit and stumbled through smoke that was filling the hotel.

They made their way to the lobby and emerged outside to find fire engines and 20 armed policemen "looking as scared as we were".

He said the Indian friend he was dining with was "still on the roof of that hotel somewhere".

A senior police officer said police are fighting the gunmen.

He said "the terrorists have used automatic weapons and in some places grenades have been lobbed".

He said: "The encounters are still going on and we are trying to overpower them."

A spokesman for the Foreign Office said he could not give any indication of the number of Britons involved in the incident and could not comment on reports that British people were being targeted.

He said the Foreign Office was advising all British nationals to stay indoors.

British national Liam Butler told the BBC that he was close to the Taj Mahal hotel when it was attacked.

"We just thought there were some fireworks, we looked up expecting to see some fireworks, but we then sort of brushed it off," he said.

However he was then unable to get back to his taxi and the news of the attack quickly spread by word of mouth between taxi drivers in the area.

Mr Butler managed to get a taxi away from the area and was later by the domestic airport when an explosion, which he described as a "taxi bomb", went off.

He said it took hours to reach the northern part of the city and it was a "very, very panicked" situation.

The Foreign Office warns travellers there is a "high threat" of terrorism throughout India.

Attacks have targeted places of worship and major festivals such as Diwali as well as areas popular with expatriates and foreign travellers.

Mumbai, known as the financial capital of India, has been among the major cities targeted in violence across the country in recent years.

On July 11, 2006 there was a series of explosions on commuter trains in western Mumbai, leaving more than 180 people dead and hundreds injured.

In some areas of the country there are terrorist incidents "virtually on a daily basis", according to the Foreign Office.

As recently as October 30, 11 bombs exploded in Assam where a 30-year insurgency campaign by an ultranationalist group is taking place, killing 77 people and injuring more than 300.

In the US, a State Department spokesman said: "We strongly condemn the terrorist attacks that have taken place in Mumbai, India.

"Our sympathies go out to the families and friends of those killed and injured, and to the people of Mumbai.

"We are monitoring the situation very closely and stand ready to support the Indian authorities as they deal with this horrific series of attacks.

"At this point, we are unaware of any American casualties."

Foreign Secretary David Miliband also spoke out against the attacks.

"Today's attacks in Mumbai which have claimed many innocent victims, remind us, yet again, of the threat we face from violent extremists," he said in a statement.

"I condemn these attacks unreservedly. Our thoughts are with the families and friends of those killed and injured.

"The UK and India will continue their joint efforts to counter the actions of terrorists."

Tory leader David Cameron said: "I utterly condemn the attacks that have taken place in Mumbai and the terrible loss of life that has occurred.

"My thoughts are with all those who have been caught up in these attacks. India and Britain stand together at this time in the face of terrorism."

Liberal Democrat leader Nick Clegg said: "Our immediate thoughts are with those families who are worried about their loved ones. Everything must be done to help them at this difficult time.

"When violent terrorism raises its ugly head, it is crucial that the international community stands together.

"India and Britain have close historical ties which should rightly prompt a signal of strong support from Britain to the Indian government."

US president-elect Barack Obama's chief national security spokesman Brooke Anderson said: "President-Elect Obama strongly condemns today's terrorist attacks in Mumbai and his thoughts and prayers are with the victims, their families, and the people of India.

"These co-ordinated attacks on innocent civilians demonstrate the grave and urgent threat of terrorism.

"The United States must continue to strengthen our partnerships with India and nations around the world to root out and destroy terrorist networks.

"We stand with the people of India, whose democracy will prove far more resilient than the hateful ideology that led to these attacks."