KABUL  - Afghan President Hamid Karzai demanded Sunday the withdrawal of US special forces from Wardak within two weeks, accusing them of fuelling ‘insecurity and instability’ in the volatile province neighbouring the capital Kabul.

"In today's national security council meeting... President Karzai ordered the ministry of defence to kick out the US special forces from Wardak province within two weeks," said presidential spokesman Aimal Faizi.

"The US special forces and illegal armed groups created by them are causing insecurity, instability, and harass local people in this province," he told a press conference. The announcement would be another blow to the prestige of US-led forces as they prepare to withdraw combat troops from the war against Taliban Islamist insurgents by the end of next year.

A US Forces Afghanistan (USFOR-A) spokesman said he was aware of the reported comments by Faizi. "We take all allegations of misconduct seriously and go to great lengths to determine the facts surrounding them," he said.

"Until we have had a chance to speak with senior (Afghan) officials about this issue we are not in a position to comment further. This is an important issue that we intend to fully discuss with our Afghan counterparts."

More than 3,200 Nato troops, mostly Americans, have died in support of Karzai's government in the war since the Taliban were ousted by a US invasion in 2001, but relations between the president and the US are often prickly.

Meanwhile, two Taliban suicide bombers killed three members of Afghan security forces on Sunday, but a third attack in Kabul's diplomatic enclave was foiled when police shot dead the would-be assailant, officials said.

The attacker in Kabul was armed with a suicide vest and his SUV was full of explosives, but police opened fire when he tried to penetrate deeper into the capital's diplomatic enclave of Wazir Akbar Khan, the officials said.

In the day's first attack, a suicide bomber rammed an explosives-laden car into a spy agency facility in the town of Jalalabad, 150 kilometres east of Kabul.

It was followed by a similar attack on a police base in Puli Alam, 70 kilometres south of the capital, officials said.

Taliban spokesman Zabihullah Mujahed claimed responsibility for the attacks in Puli Alam and Jalalabad, but denied that the militant group was involved in the foiled attack in Kabul.

Authorities had earlier said that two would-be suicide bombers were killed in Kabul. But city police chief Mohammad Ayoub Salangi said only one attacker was involved, dismissing local reports that a second bomber had managed to escape. "We have intelligence about this. The bomber was shot dead and his car bomb is defused. It's over now," Salangi told AFP. An AFP photographer at the scene saw a young man laying dead in a pool of blood next to his bullet-ridden car on the side of the road near a construction site. The man was shot in the head.

The same construction site was overrun by insurgents as part of a coordinated attack in Kabul and several other provinces in April 2012. In Jalalabad, police spokesman Hazrat Hussain Mashriqiwal said the bomber rammed his sedan car into the gates of the walled compound of a National Directorate of Security branch and detonated his bombs.

"There was a suicide car bombing in the intelligence facility in city district two. Two intelligence workers were martyred and three others were wounded," Mashriqiwal said.

Police in Puli Alam, the capital of Logar province, said the attack there hit the gates of a police base along the highway leading to Kabul and killed one police officer.

Logar police chief Abdul Saboor Nasrati said the bombing was carried out in a van and caused "a massive explosion" that broke glass and caused damage to nearby homes.

The Taliban have waged an 11-year insurgency against the Kabul government since being ousted from power in a US-led invasion in 2001.

The United States and Nato have around 100,000 troops in Afghanistan, but the vast majority of them will leave next year, with Afghan forces progressively taking over.