Iran wants all foreign forces to leave Afghanistan, President Hassan Rouhani told his visiting Afghan counterpart Sunday amid a row between Kabul and Washington over a long-delayed security pact.

Iran "is opposed to the presence of any foreign force in the region, the Middle East, the Persian Gulf and particularly the Islamic country of Afghanistan," Rouhani told Hamid Karzai, who was in Tehran for a one-day visit.

"Iran is concerned about tensions caused by the presence of foreign forces in the region," Rouhani added in remarks reported by the state broadcaster on its website, iribnews.ir.

Washington and its allies have urged Karzai to sign the Bilateral Security Agreement (BSA), which would establish the legal conditions for US and other NATO troops to remain in Afghanistan past 2014 to train local security forces and fight Al-Qaeda.

Karzai initially endorsed the BSA, but has since refused to sign it and issued fresh demands.

Karzai's trip to Iran came a day after an awkward visit to Kabul by US Defence Secretary Chuck Hagel, who did not meet with Karzai as is customary, saying the Afghan leader was well aware of the US position on the pact.

Tehran -- which has long been wary of the tens of thousands of US troops based in Afghanistan and in large military bases in the Gulf -- has strongly backed Karzai's position on the pact.

"They should all leave and leave the security of Afghanistan to its own people," said Rouhani.

Iran is meanwhile hoping to sign a security pact of its own with Kabul.

Rouhani and Karzai agreed to begin negotiations over a "Comprehensive Friendship and Cooperation Agreement" which would also involve political, economic and cultural affairs, according to the official IRNA news agency.

Details of the deal were not immediately available to the media.

In Kabul, the two sides signed a separate border and security agreement, an Iranian deputy interior minister said.

That agreement establishes "a joint committee on terrorism, security related organised-crimes as well as controlling the borders to fight human trafficking, (illegal) immigration and drug smuggling," Ali Abdollahi told IRNA.

Iran shares a 936-kilometre (582-mile) border with Afghanistan and hosts some 2.4 million Afghans -- refugees and illegal immigrants -- who were driven across the border by war, oppression and poverty over the past three decades.