LONDON, August 10. /TASS/. British Prime Minister Theresa May spoke with Russian President Vladimir Putin by telephone on Tuesday, marking the importance of relationship between the two countries, a Downing Street spokesperson said.

"The Prime Minister noted the importance of the relationship between the UK and Russia, and expressed the hope that, despite differences on certain issues, they could communicate in an open and honest way about the issues that mattered most to them," the spokesperson said.

"The Prime Minister and President agreed that British and Russian citizens faced common threats from terrorism, and that cooperation on aviation security in particular was a vital part of the international counter-terrorism effort. They looked forward to seeing each other at the G20 summit in China next month," the spokesperson added.

The Kremlin said "The sides discussed current issues of the Russian-British relations and expressed dissatisfaction with the current cooperation parameters. They agreed to invigorate joint work in a number of areas."

Theresa May "confirmed Britain’s high-level participation" in the celebrations of the 75th anniversary of the arrival of the first British Arctic convoy to Russia’s northern port of Arkhanglesk several weeks after Nazi Germany’s invasion of the Soviet Union.

The Russian president once again congratulated Theresa May on her appointment to the post of Britain’s prime minister.

Theresa May, 59, was officially appointed UK Prime Minister on July 13, after David Cameron's resignation. He stepped down after the national referendum on EU membership when the majority of Britons voted for Brexit.