Theresa May has spoken to Russian president Vladimir Putin for the first time since she became Prime Minister.
The Kremlin said both leaders expressed dissatisfaction with UK-Russian relations and pledged to improve ties.
The UK's relationship with Russia became increasingly strained under former prime minister David Cameron, following Mr Putin's support for the Syrian regime, the Ukraine crisis, and the recent inquiry in to the 2006 poisoning death of ex-Russian spy Alexander Litvinenko.
Mrs May said she hoped the nations could push forward in an "honest" way despite their differences. The pair will meet at the G20 summit of world leaders in China next month.
A Downing Street spokeswoman said the leaders discussed common security threats faced by both countries when they spoke on the phone on Tuesday afternoon.
She 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 Prime Minister and president agreed that British and Russian citizens faced common threats from terrorism, and that co-operation 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 pair agreed to develop a dialogue between their security agencies over aviation security, the Kremlin added.
The Russian government said Mrs May also confirmed Britain's intention to participate in the 75th anniversary of the first arrival of vital aid by British wartime convoys to the Russian city of Arkhangelsk, later this month.
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