David Cameron and Russian president-elect Vladimir Putin spoke tonight about developing a "stronger relationship" despite "differences and areas of concern".
Amid protests in Moscow and allegations of corruption in the presidential contest, the Prime Minister told Mr Putin he had been "following the Russian elections closely", Downing Street said.
He pointedly avoided congratulating the president-elect. In a statement, a Number 10 spokesman said Mr Cameron had called Mr Putin this evening.
"The Prime Minister said that he had been following the Russian elections closely," the spokesman said.
"He looked forward to working with Mr Putin to overcome the obstacles in the relationship between Britain and Russia and build deeper political and trade links. The leaders agreed on the importance of building a stronger relationship, without disguising differences and areas of concern."
The spokesman said Mr Cameron and Mr Putin also discussed the situation in Syria and "the need for united international action to bring an end to the violence and prevent the situation deteriorating into civil war".
The Prime Minister has been highly critical of Russia's stance on Syria so far.
The protest outside the central election commission was organised by the Other Russia movement.
National Bolshevik Party leader Eduard Limonov was arrested at the protest, along with about 50 supporters, Moscow police said in a statement.
Earlier, Downing Street acknowledged the presidential elections had delivered "a decisive result" in favour of Mr Putin.
While there had been "some problems" with the election, the overall outcome was not in doubt, Mr Cameron's official spokesman said.
Mr Putin last night claimed victory with more than 60% of the vote, despite opposition claims of widespread vote rigging and electoral fraud.
However, Mr Cameron's spokesmen said even independent assessments of the count had put Mr Putin clearly ahead.
"It is clear that the election has delivered a decisive result," the spokesman said.
"Even the NGO (non-governmental organisation) polling data put Putin above the 50% needed to win in the first round.
"It is right that these assessments have taken place. They have clearly identified some problems. We would like to see these issues addressed over time."
An observer mission from the Organisation for Security and Co-operation in Europe concluded there were "serious problems" in the way the election was conducted.
The head of the mission, Tonino Picula, said: "There was no real competition, and abuse of government resources ensured that the ultimate winner of the election was never in doubt."
Among the string accusations of violations is ballot-stuffing, with footage released by the Associated Press appearing to show officials feeding stacks of paper into a voting machine.
Police are braced for public disorder once the vote closes following unprecedented mass protests over Mr Putin's system of so-called "managed democracy".