Pompeo will talk about Afghanistan with alliance Secretary General Jens Stoltenberg on Tuesday, a day after the US envoy leading efforts to strike a deal with the Taliban to end 18 years of war showed the draft peace agreement to the Kabul government.

Under the deal, the US will withdraw troops from five bases in Afghanistan within about four months of it being approved, provided the Taliban stick to their commitments, though President Donald Trump last week said America would maintain a permanent presence -- with 8,600 troops initially -- in any event.

A NATO official said Stoltenberg and Pompeo would discuss "current security issues and preparations for upcoming meetings", including the alliance's summit in London in December.

"We expect they will also discuss the peace process and the NATO-led mission in Afghanistan," the official said.

NATO ended its combat mission in Afghanistan in 2014 but maintains some 16,000 troops on a mission to train, advise and assist local forces.

The US invaded Afghanistan in the wake of the September 11, 2001 terror attacks, ousting the Taliban from power, but while the country has seen substantial improvements in many fields, the security situation remains volatile.

Both Washington and the alliance insist that their priority is to ensure Afghanistan does not become a haven for extremists, with particular concerns about the influence of the Islamic State group, which killed at least 80 people at a wedding in Kabul last month.

Aside from the NATO meeting, Pompeo will meet the incoming European Commission chief Ursula von der Leyen on Monday evening, as well as new EU diplomatic chief Josep Borrell and EU Council President Charles Michel.

"Headed to Brussels to meet with #NATO and #EU leaders to discuss Transatlantic cooperation on economic and security issues. We can do more together through meaningful, effective multilateralism," Pompeo tweeted as he left the US.

The tweet suggests a push to reset US-EU ties which have frayed since Trump took office, with Washington and Europe differing strongly on a host of issues from the Iran nuclear deal and climate change to trade and international institutions.

An EU spokeswoman said it would be an "introductory meeting".