The two men hoping to be Ukraine's next leader have met and agreed to try to negotiate an end to the dispute over Sunday's presidential election.
Tensions are rising on the streets of Ukraine's capital, Kiev
Prime Minister Viktor Yanukovych and opposition leader Viktor Yushchenko have set up a working group to discuss possible solutions.
Mr Yushchenko says the poll's second round must be re-run. Mr Yanukovych wants the issue resolved in court.
President Bush said the international community was watching the situation.
"People are paying very close attention to this, and
hopefully it will be resolved in a way that brings credit and confidence to the Ukrainian government," he said.
The talks were hosted by outgoing President Leonid Kuchma and attended by European and Russian mediators.
The mediators include EU foreign policy chief Javier Solana, Polish President Aleksander Kwasniewski, Lithuanian President Valdas Adamkus and Russian parliamentary Speaker Boris Gryzlov.
Mr Yushchenko, who favours closer ties with the West, said he would take action within days if negotiations failed.
In a BBC interview, he said the opposition would bring two million people out onto the streets.
"We will allow only a few days for the negotiation process. If
Yanukovych wants to drag things out, we will
take active measures," he told supporters in Independence Square in the capital Kiev after three hours of mediation talks.
Tens of thousands of opposition supporters continue to demonstrate in the capital.
Protests have mostly been peaceful, but police reportedly fired tear gas over the heads of Yushchenko supporters outside the city council building in the northern city of Chernihiv.
Mr Yushchenko's party wants the repeat vote to be held on 12 December.
Mr Solana told CNN a re-run of the election's second round was "a possibility" and would be discussed by the working group.
It was the first time the rivals had met since standing against one another in the disputed election.
Russian Foreign Minister Sergei Lavrov has expressed concern about foreign involvement in the crisis.
"In some European capitals, there are some forces that are attempting to draw some new border lines across Europe," he said.
It was reported that another member of Ukraine's central election commission had withdrawn her signature from the country's official presidential election results, leaving 10 of the 15 names on the document, Ukrainian news agencies say.
Yanukovych (left): 49.46%
Western observers report:
Abuse of state resources and "overt media bias" in favour of Mr Yanukovych
State workers pressured to give absentee voting certificate to their superiors
Intimidation at some polling stations
Suspiciously high turnout - 96% - in the key pro-government region of Donetsk
The official results have to be signed by a majority, or eight members of the commission, to remain valid.
In Kiev, Prime Minister Yanukovych has accused the opposition, which has been blocking access to government buildings, of attempting to stage a coup.
He told a large crowd of his supporters in Kiev that they should do everything they could to stop it.
More than 10,000 are demonstrating at the city's railway station, and are said to be awaiting his instructions.
Parliament has announced it will hold an emergency debate on Saturday to discuss the political crisis.
According to the official election result, the pro-Russian Mr Yanukovych won with 49.46% of the vote against Mr Yushchenko's 46.61%.
But both Mr Yushchenko and independent observers reported widespread abuses.
Ukraine's Supreme Court suspended the presidential poll result on Thursday to consider the opposition's complaints.