The United States Afghan peace envoy and Pakistan's army chief have held talks to discuss the commencement of a peace process between the Afghan government and the Taliban, according to a statement, as violence has recommenced after a brief ceasefire was announced two weeks ago.

US Special Representative for Afghan Reconciliation Zalmay Khalilzad met with Pakistani army chief General Qamar Javed Bajwa in Islamabad on Sunday, the US and Pakistan's military said in separate statements.

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"The two took note of recent progress created by the Eid ceasefire and accelerated prisoner releases as well as reduced violence ahead of intra-Afghan negotiations," said the US statement on the meeting, released on Monday.

The US said Khalilzad "expressed his appreciation" in Pakistan's role of bringing the Taliban to the negotiating table.

"The two agreed peace in Afghanistan offers an unprecedented opportunity to advance security, connectivity and development for the region," said the US statement.

A Pakistani military statement on the meeting added that the issues of repatriating more than two million Afghan refugees resident in Pakistan for decades and management of the two countries' 2,500-km long border were also discussed.

Pakistan began fencing the border to curb the movement of Taliban fighters three years ago, a move that the Afghan government has rejected as it disputes the position of the border.

In February, the US and Afghan Taliban signed an historic agreement aimed at ending the US's longest war, fought in Afghanistan since 2001.

The agreement signed in the Qatari capital Doha, called for the gradual withdrawal of US troops by next year in return for security guarantees from the Taliban. It also called for a prisoner swap between Kabul and the Afghan armed group.

The Taliban-US deal excluded any representation from the Afghan government, but envisaged negotiations between Kabul and the Taliban.

After initially rejecting some of the conditions of the deal outright, the Afghan government has softened its stance in recent weeks, allowing the release of a number of Taliban prisoners.

On May 23, a three-day ceasefire agreed between the two sides for the Muslim festival of Eid extended for almost a week before violence broke out again.

On Friday, the US announced that it had recommenced air raids on the Taliban, targeting fighters and commanders in western Farah and southern Kandahar provinces.

The air raids came days after a roadside bomb killed seven civilians in northern Kunduz province and a mosque blast in the capital, Kabul, left two dead.