Medical staff at the base have been trying to save victims

Mr Cheney, who was unharmed, was staying at the Bagram base near Kabul.

The US military said the bomber was also killed. Some reports say 14 people died - more than 20 others were hurt.

The Taleban said they carried out the attack and that the attacker was trying to get to Mr Cheney, who was on an unannounced visit to the region.

A US spokesman described it as a "direct attack" on the base, which was put on red alert for a while.

Mr Cheney was said to be safely inside the compound at the time. He described hearing a "loud boom" and told reporters he had been briefly moved to a bomb shelter.

One US and one South Korean soldier were among the dead as well as a US government contractor who was a US national.

The others killed were Afghan civilians, many of whose distraught relatives gathered later outside the base.

Base operations commander Lt Col James Bonner said the bomber could not have got inside the base, 60km (40 miles) from Kabul.

"Our security measures were in place and the killer never had access to the base," he said in a statement.

"When he realised he would not be able to get onto the base he attacked the local population."

Talks delayed

Mr Cheney had breakfast with troops at the base and left about 90 minutes after the blast.

Mr Cheney met President Karzai after the blast

He held talks with President Hamid Karzai in Kabul on the deteriorating security situation before flying out of the country. It was "never an option" to scrap the talks, he said.

Shortly before the Bagram blast, there was another suicide bomb in the southern city of Kandahar, killing at least one person.

Elsewhere, Nato said it had killed three civilians in clashes in the south.

One person was shot dead by Nato troops in "self defence" near Kandahar on Tuesday, while two others had been hit by mortar fire in Helmand province a day earlier, a statement said.

The BBC's Charles Haviland in Kabul says Bagram is one of the most heavily guarded sites in Afghanistan and such incidents there are extremely rare.

The surrounding territory is heavily mined and people, including children, have frequently been injured by such devices.

Officials said the explosion occurred between the outside security gate and an inner gate guarded by US troops, some distance from living quarters at the base.

A trader in a market outside the base described the explosion as "huge", saying it shook market stalls.

Tough message

Mr Cheney's visit came amid increasing concern about insurgent activity in several areas of Afghanistan.

Pakistan has thousands of troops near the border

There are 27,000 US troops in Afghanistan, the highest number since the invasion of 2001, to combat any offensive.

Mr Cheney arrived in Afghanistan on Monday after holding talks with Pakistani President Pervez Musharraf during a brief stop in Islamabad.

He urged Pakistan to do more to combat the Taleban near the Afghan border, but also praised its role in the "war on terror".

His visit comes as the US seeks to send a tough message to Pakistan that aid to the country could be cut unless efforts to catch militants are stepped up.

Afghanistan and Pakistan share a 1,400-mile (2,250km) border, and many Taleban fighters operate from bases on the Pakistani side.