NATO has urged Afghanistan to accelerate the signing of a strategic partnership deal with the US in the wake of deadly protests over the burning of the Koran, President Hamid Karzai said Wednesday.

NATO secretary general Anders Fogh Rasmussen made the appeal in a telephone call to Karzai in which he expressed regret over the deaths of dozens of demonstrators in anti-US protests, Karzai's office said.

In response, the Afghan president said he was willing to sign the long-term agreement but reiterated that it would only be done under certain conditions.

These include a respect for Afghan national sovereignty, an end to night raids by international forces and the handing over of the Bagram prison -- known as Afghanistan's Guantanamo Bay -- to Afghan control, Karzai said in a statement.

Rasmussen had said the signing of the partnership deal, which covers relations with the US after it withdraws its combat troops in 2014, would make a "good impact" on the Chicago conference on Afghanistan in May.

The NATO chief insisted in a statement Tuesday that trust had not broken down between alliance-led troops and Afghan security forces, despite incidents in which Afghans turned their weapons on their American partners.

Two US military advisers were gunned down in the interior ministry in Kabul on Saturday, days after two American troops were killed by an Afghan soldier in the east, prompting NATO to pull its advisors out of Afghan government ministries.

Popular outrage erupted after Afghans learned that copies of the Koran were thrown into an incinerator pit at the US-run Bagram airbase, leading US President Barack Obama to apologise for what he described as an error.

Rasmussen accused Islamist insurgents of attempting to exploit anger over the Koran burning and said he hoped that NATO military advisers would soon return to their posts at Afghan government ministries.

NATO has a 130,000-strong US-led military force fighting the Taliban, which has led an insurgency against the Western-backed Kabul government since being toppled from power in 2001.