Britain's Foreign Secretary Boris Johnson has called for "dialogue" to resolve the current dispute between Qatar and four other Arab states and reiterated London's support for Kuwait's mediation efforts to end the rift.

Johnson made the call during a meeting with Kuwait's foreign minister in the Kuwaiti capital on Saturday, according to its state news agency KUNA.

"My impression is that progress can be made ... But I am not going to pretend that it is going to be overnight," Johnson said after the meeting.

The two disputing sides have not met yet, but "let's keep our fingers crossed, let's keep working for common sense and for de-escalation on both sides", he added.

"There's no possibility of a military escalation," he said.

"We are working, supporting our Kuwaiti friends to get an understanding of how to take forward a wider fight against the financing of terrorism not just by Qatar, but by all our friends in the region."

Qatar visit

Later on Saturday, Johnson travelled to Doha where he held a meeting with Qatar's Emir Sheikh Tamim bin Hamad Al Thani and the country's senior officials.

According to Qatar's state news agency, they discussed the Gulf crisis as well as ways to enhance counterterrorism cooperation between Doha and London.

Johnson's talks in Kuwait and Qatar came a day after he held meetings on Friday with officials from Saudi Arabia and the United Arab Emirates - two leading actors in the dispute.

US Secretary of State Rex Tillerson is also due in Kuwait with a similar mission on Monday.

READ MORE: All the latest updates about the Gulf crisis

On Friday, Qatar again rejected accusations that it finances "terrorism" and interferes in the domestic affairs of other countries after the four Arab states boycotting it - Saudi Arabia, Egypt, Bahrain and the UAE - threatened further measures.

The quartet cut diplomatic and transportation links with Qatar in early June, accusing Doha of supporting "terrorism" and later issuing a list of 13 demands to the country.

They included downgrading ties with Iran, a regional rival of Saudi Arabia, and shutting down the Doha-based Al Jazeera Media Network.