US Secretary of State John Kerry met Saudi King Salman on Sunday ahead of a week of crunch talks on the conflicts in Syria and Libya.

Riyadh has been a key supporter of rebels fighting to overthrow the Damascus regime of President Bashar al-Assad.

Its allies Cairo and Abu Dhabi have also been major supporters of the administration in eastern Libya which is still withholding its support from a UN- and US-backed unity government in Tripoli.

In talks with his Saudi counterpart Adel al-Jubeir, Kerry discussed "regional issues... mainly developments in Syria," the official Saudi Press Agency reported.

"I want to thank you for the many things that Saudi Arabia is working on with us to great effect," he said.

Kerry was to fly to Vienna later on Sunday for the meetings on Libya and Syria on Monday and Tuesday.

On Wednesday, he will fly on to Brussels for a Nato foreign ministers' meeting and talks on the full range of challenges facing the Western allies.

Kerry's spokesman John Kirby said the secretary of state and Italian Foreign Minister Paolo Gentiloni would jointly host the Libya conflict meeting.

Participants will "discuss international support for the new Government of National Accord, with a focus on security," Kirby said.

The unity government was formed after months of negotiation by UN mediators in a bid to end the chaos of rival administrations in the east and west of Libya that had undermined the fight against the Islamic State group.

It has slowly asserted its authority in Tripoli since late March taking over key institutions like the central bank and the National Oil Corp but it still faces a rival administration in the east.

Officials say the fledgling regime is drawing up a list of requests for Western partners to assist its forces with arms, training and intelligence.

After the Libya meeting, Kerry and Russian Foreign Minister Sergei Lavrov will lead a meeting of the 17-nation International Syria Support Group.

Kirby said the goal was to "ensure humanitarian access throughout the country, and to expedite a negotiated political transition in Syria."

The ISSG, under the odd couple of Kerry and Lavrov, is pushing Syrian President Bashar al-Assad's regime and a coalition of opposition groups to respect a shaky truce in force since February.

Officials hope next week's meeting will inject new life into the peace process and - if the ceasefire holds - secure talks on forming a unity government.

And, with Russia and France, Kerry will also co-chair a meeting on the Nagorno-Karabakh conflict between the presidents of Armenia and Azerbaijan.