The move by Putin on Thursday underlines Kremlin fears that if Ukraine's opposition presidential candidate Viktor Yushchenko takes power, he would weaken links with Moscow and push Ukraine deeper into the West's embrace.
Alleging the election was rigged, the opposition wants an early repeat of the 21 November run-off vote between Yushchenko and former prime minister Viktor Yanukovich.
Kuchma, who flew to Moscow on Thursday, wants a completely new election rather than just a repeat of the recent run-off between the two candidates, a longer process which could favour his candidate.
He said, however, he was prepared to speed up the process.
"A repeat of the run-off vote may fail to work," Putin told Kuchma at an airport meeting outside Moscow.
"A repeat of the run-off vote may fail to work"
Russian President Vladimir Putin
In a sign of the strain the crisis is placing on relations as Russia and the West vie for influence in Ukraine, US President George Bush took a swipe at Moscow's involvement, saying outsiders should not meddle in a new election.
"I think any election, if there is one, ought to be free from any foreign influence. These elections ought to be open and fair," Bush said.
Meanwhile, Polish President Aleksander Kwasniewski has joined the fray on the side of the opposition.
"We need to repeat the second round between the same candidates and give Ukrainians a chance to make a free choice. Once we secure fairness of the procedure we will be sure that democracy has won," he told TVN24 television.
Ukraine's supreme court was holding its fourth day of deliberations on Yushchenko's accusations the election was rigged, with a ruling expected on Friday.
Regional leaders took part in
mediation talks this week
Yushchenko, addressing tens of thousands of supporters standing outdoors in sub-zero weather late in the evening, reiterated his opposition to holding a new poll from scratch.
"Let me say this to Kuchma, to anyone, to any politician calling for a fresh election - this amounts to calling for the economic collapse of Ukraine," he said in a 40-minute speech at Kiev's Independence Square.
He urged demonstrators to stay put in the square.
Struggle for influence
The crisis has turned into a struggle for influence in potentially wealthy Ukraine between the West, which leans towards Yushchenko, and Russia, which prefers Yanukovich.
Putin last week congratulated Yanukovich - whose campaign he helped - on his win even before it was official, amid international charges that the poll was fraudulent.
"Let me say this to Kuchma, to anyone, to any politician calling for a fresh election - this amounts to calling for the economic collapse of Ukraine"
Opposition candidate Viktor Yushchenko
With the next move focusing on the staging of an election of some sort, Ukraine's politicians have agreed to wait for the supreme court decision on Friday.
If the court rules that the election was not legitimate, the central election commission will probably call a new poll.
What kind of poll that will be, is now the focus of dispute.
But there is mounting speculation that if he gets his way, Kuchma will drop Yanukovich, who was sacked by parliament as prime minister on Wednesday.
In another sign he may be seeking an alternative candidate, Kuchma told ministers he would dismiss them if parliament proceeded with reforms to give the government more powers.
"We urgently need to implement political reform. The government will be dismissed and there will be a new government. The most important thing for Ukraine now is to have a working government."