The US President Donald Trump says he called his Russian counterpart Vladimir Putin to congratulate him on his election victory.
During a meeting at the White House with the Saudi Crown Prince Mohammed bin Salman, Mr Trump told reporters he believed he and Mr Putin would meet "in the not too distant future".
Mr Putin was re-elected by a landslide, with more than 76 percent of the vote. It will be his fourth 6-year term. But there was no strong challenger with the main opposition leader Alexei Navalny barred from the race.
Mr Trump said the arms race between the US and Russia was "getting out of control ... but we will never allow anybody to have anything close to what we have".
But he did not mention the issue that has sparked growing Western tensions with Moscow - the poisoning of ex-spy Sergei Skripal and his daughter Yulia in Britain.
The UK government blamed the nerve agent attack on Russia, which denies any involvement. As a result, 23 Russian diplomats were expelled from the UK.
In retaliation Moscow then ordered 23 British diplomats to leave Russia.
US Senator John McCain criticised Mr Trump for congratulating Mr Putin on his election victory.
"An American president does not lead the free world by congratulating dictators on winning sham elections. And by doing so with Vladimir Putin, President Trump insulted every Russian citizen who was denied the right to vote in a free and fair election to determine their country's future, including the countless Russian patriots who have risked so much to protest and resist Putin's regime," McCain said in a statement.
EU Commission chief Jean-Claude Juncker wrote a letter of congratulations to the Russian leader on Tuesday, pledging to "always be a partner" in improving security co-operation with the Kremlin.
"I have always argued that positive relations between the European Union and Russian Federation are crucial to security of our continent," he said in the letter, which he shared on Twitter.
German Chancellor Angela Merkel was among the first Western leaders to "warmly congratulate" Mr Putin on Monday - a day after his re-election - stressing the need to continue dialogue "to address important bilateral and international challenges and find viable solutions".
- BBC