The Kremlin says Russia's President Vladimir Putin has spoken to British Prime Minister Theresa May for the first time since she took office.

In Tuesday's call, both leaders "expressed dissatisfaction with the current parameters of cooperation in both the political and economic sphere," according to the Kremlin.

Russian-British ties have been strained by the 2006 poisoning death of ex-Russian spy Alexander Litvinenko, the Ukraine crisis and other issues.

The Kremlin said Putin and May agreed to develop a dialogue between security agencies on issues related to aviation security, and made plans for a personal meeting in the "near future."

It noted that May confirmed Britain's intention to participate in ceremonies marking the 75th anniversary of the arrival of the first British WWII convoy in the Russian city Arkhangelsk this month.