"I believe that Yeltsin has a very good chance of being elected in the second round, and I hope that is true," said Denmark's Foreign Minister, Niels Helveg Petersen. "It's been a difficult reform process, and it will continue to be difficult, but now it's on the right track."
Despite disagreements with Mr Yeltsin over issues such as Nato's planned enlargement into central and eastern Europe, Western leaders had made it plain before Sunday's vote that they greatly preferred the President to Mr Zyuganov. The Communist candidate is viewed with suspicion because of his calls for the Soviet Union's restoration, his past association with militant, anti-democratic Russian nationalists, and his apparent inclination to halt or reverse many of Mr Yeltsin's economic reforms.
For the West, much hinges on a Yeltsin victory in the second round. If he wins, it may be possible to achieve a compromise on Nato's enlargement, with the alliance taking in the Czech Republic, Hungary and Poland but agreeing not to turn these countries into "forward bases" filled with Nato troops and weapons pointed at Russia.
The West also believes that a Yeltsin victory offers the best chance of maintaining the Russian economic recovery that began last year and is underpinned by a $10.2bn (pounds 6.5bn) loan from the International Monetary Fund. The hope is that steady economic progress, based on flourishing private enterprise, should consolidate Russian democracy and make it less vulnerable to extremist challenges.
However, Germany's Foreign Minister, Klaus Kinkel, drew attention to the strong performance of Alexander Lebed, the retired army general who campaigned on law and order and a revival of Russian national pride. Mr Lebed's score of almost 15 per cent was "a sign of discontent in the Russian electorate", Mr Kinkel said.
Nato officials said they were untroubled by the fact that the combined vote for Mr Zyuganov, Mr Lebed and the ultra-nationalist, Vladimir Zhirinovsky, was slightly over 50 per cent. The main features of the West's relationship with Russia - broadly constructive co-operation, coupled with frostiness over individual issues - were likely to stay in place, despite the considerable popularity of Russian politicians who emphasise "national greatness" ahead of democracy and economic reform.
There was unanimous delight at the relatively poor performance of Mr Zhirinovsky, who left Western leaders speechless with dismay in December 1993 when his party triumphed in parliamentary elections. "It is a great deal more preferable that Lebed take 15 per cent and see himself as a king-maker than Zhirinovsky," one European official said.
Among the 1,100 international observers who monitored Sunday's voting, there was general agreement that the election had been free and fair. However, a delegation from the Organisation for Security and Co-operation in Europe (OSCE), which contributed about half of all the observers, expressed concern at biased coverage in the state-owned Russian media.
This appeared to refer to the way that Russian television in particular concentrated on the progress of Mr Yeltsin's campaign, while limiting coverage of Mr Zyuganov or presenting him in a less favourable light. "The delegation trusts that the Central Electoral Commission will investigate these issues and, if necessary, take appropriate action to prevent them occurring in the future," an OSCE statement said.
President Bill Clinton congratulated Mr Yeltsin on a "strong showing" in the election. "This is a very significant thing for Russia to have this election," Mr Clinton said. "The Russian people and Russian leadership are to be complimented for supporting the constitution and the elective process."