Afghan President Ashraf Ghani on Tuesday played down recent failures to jump start peace talks with the Taliban, instead choosing to highlight recent successes against the nascent Islamic State presence in Afghanistan.

Taliban forces have made significant gains in recent months, briefly capturing the northern city of Kunduz and threatening to overrun multiple districts in the southwest.

The latest efforts to bring them to the negotiating table faltered when the militant group issued a statement refusing to participate.

Ghani, facing rising domestic criticism and eager to ensure continued international aid, has publicly focused on a military campaign in eastern Afghanistan aimed at Islamic State, often referred to as Daesh, which has struggled to replicate its successes in Iraq and Syria.

"Daesh is on the run," he said at a joint news conference with Nato Secretary General Jens Stoltenberg, responding to a direct question about the Taliban. "They are running for cover."

"No quarter would be given" to Islamic State fighters, Ghani added. A combination of air strikes by US warplanes and "massive" ground operations by Afghan forces has left Islamic State reeling, he said.

Stoltenberg reiterated that the coalition has no intention of sending combat troops back to fight in Afghanistan, more than a year after the Nato-coalition declared an end to its combat mission.

Thousands of coalition troops remain to train and advise Afghan forces, but operations are limited to self-defence. A US counterterrorism force continues to conduct air strikes and special forces raids on suspected militants, including those of Islamic State.

In July, Nato officials will meet in Warsaw to determine the future of funding for 2018 through 2020, as well as other issues such as foreign troop levels, which have been thrown into flux as the coalition seeks to prop up the struggling Afghan forces.

Before that, however, international backers are looking for Kabul's leaders to fight corruption, modernise institutions, reform the electoral process, and protect human rights, Stoltenberg said during his visit to the Afghan capital.

"The single most important thing we would like to see is that Afghanistan continue to implement reforms," he said, adding that the more progress is made, the more likely it will be that coalition partners will commit to continued funding and troops.

Nato has pledged to provide $5.1bn per year to Afghanistan through 2017.

"The more that we see Afghanistan is able to fight corruption, the easier it will be for me and other political leaders to mobilise the necessary political support," Stoltenberg said.