US Secretary of State Mike Pompeo pressed Afghanistan's Taliban to come to the table to end the long-running war as he called on Pakistan to play a supportive role, the State Department said on Wednesday.

Pompeo met Foreign Minister Shah Mehmood Qureshi in Washington, in the latest US outreach to the government of Prime Minister Imran Khan.

The top US diplomat, who met Khan last month in Islamabad, “emphasised the important role Pakistan could play in bringing about a negotiated settlement in Afghanistan,” State Department spokeswoman Heather Nauert said.

Pompeo “agreed that there was momentum to advance the Afghan peace process, and that the Afghan Taliban should seize the opportunity for dialogue,” Nauert said of the meeting, which took place Tuesday.

President Donald Trump has doubled down on the war effort in Afghanistan despite his past calls to end the longest-ever US war.

But diplomatic efforts have also intensified, with US officials meeting in July in Qatar with representatives of the Taliban, whose hardline regime was overthrown in a US-led operation in the wake of the September 11, 2001 attacks.

The State Department notably did not say whether Pompeo addressed Pakistan's position on extremism.

In August, Pompeo congratulated Khan in a telephone call on taking office, with the State Department saying that he asked Islamabad to “take decisive action against all terrorists operating in Pakistan”. Islamabad denied the account, saying that the issue never came up.

According to a statement issued by the State Department, Pompeo told Qureshi that the US looked forward to working with the new Pakistani government.

"Secretary Pompeo discussed the importance of the United States and Pakistan working together to advance joint priorities, recognising that bilateral cooperation was mutually beneficial and a factor for stability in South Asia," it said.

Pompeo and Qureshi resolved to remain engaged on these and other issues, and reiterated their desire to "maintain constructive dialogue to advance shared interests".

Qureshi and Pompeo first met in Islamabad early last month as the US approached the new government to hear its views on the key issues that have strained decades-old ties between the two countries.

Pompeo, asked at a recent briefing about the US decision to re-engage Pakistan, said Islamabad elected a new leader this July, and “(we) wanted to get out there at the beginning of his (Imran Khan’s) time in an effort to reset the relationship between the two countries.”

It was during the Islamabad visit that Pompeo invited the Pakistani foreign minister to visit Washington for further talks.