But it seems neither the pro-Western opposition nor the government-backed side can find common ground for holding talks with one another.
Last night, it seemed there might be a breakthrough in the impasse when Yushchenko and two senior colleagues in his Our Ukraine coalition, Yuliya Tymoshenko and Oleksandr Zinchenko, showed up for what they thought would be talks with outgoing President Leonid Kuchma.
No details were given about what happened but the talks did not occur.
Today, Yanukovych announced he was ready to talk to the opposition camp. But the opposition insist they will only speak to Kuchma. The outgoing president himself -- who backs Yanukovych -- has mostly been silent but says the two sides should talk.
Roman Zvarych is an Our Ukraine member of parliament who has been the coalition's representative at the Central Election Commission and will be part of any negotiation team with the government. He said many things still have to be clarified regarding his group's strategy regarding talks, but that he hoped to see some decisions by the end of today.
"At the moment we are formulating our position on this matter -- whether we are ready to hold talks, in what form, with whom and most importantly on what subject," he said.
But he said his side would put preconditions on any talks -- including that it will only engage in discussions if Kuchma heads them himself.
Some observers have suggested that the two would-be winners of Ukraine's presidential race should work together -- for example, with Yanukovych as president and Yushchenko as prime minister. But Zvarych said he believes that is unlikely.
"If the other side thinks that we are ready to sit down around a table and discuss the possibility of Yanukovych remaining president or to discuss any other compromises, well, that possibility is excluded," Zvarych said.
One of Yanukovych's party members, parliamentarian Mykola Hapochka, suggests his side could be equally uncompromising.
"The results of the Central Election Commission will be precise and they are the only ones who will name the president -- and everyone else, please, obey his decrees and orders," Hapochka said.
Another parliamentarian and adviser to the Yanukovych campaign, Taras Chonovil, said that, under the law, talks between Kuchma and the opposition would not alter anything.
"No recount can happen, at least in principle, it's forbidden by law. Appealing to the president, to the parliament or the Central Election Committee is forbidden," Chornovil said. "The law says that under any circumstances the president cannot interfere in the results of an election. He cannot change the election result. Therefore, those calling people out into the streets right now, that group that wants to divide [the country] they don't have a realistic basis."
The head of Ukraine's Supreme Court, Mykola Shelest, advised Yushchenko to appeal to the Supreme Court to rule as invalid the results from polling stations where the opposition charges there was fraud.
Meanwhile, it is starting to snow harder in Kyiv yet thousands of demonstrators are continuing to stay overnight in tents pitched on the capital's main Khreschatyk Street.
Our Ukraine parliamentarian Zvarych said that bad weather will not discourage the protestors.
"We are prepared to go on for as long as necessary," Zvarych said. "There is no way that we are going to obey a criminal government. The people who support us are of exactly the same point of view and have shown that and we are convinced that the number of these people who are taking part in this, so far peaceful, nationwide insurrection will only grow."
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