How serious he is about this is not yet clear, since he himself recently declared his opposition to a fresh ballot. The options though are narrowing fast.
Former Prime Minister Yuliya Tymoshenko has no such inhibitions.
She told the Boston-based "Christian Science Monitor" on July 12 that the parliament has betrayed its promises to the people and is therefore illegitimate. There are two possibilities, she said: either we "become the coalition ourselves, or, if the law allows it, we will definitely be in favor of holding an early election."
Perhaps because it senses public opinion swinging in its favor, the Party of Regions is also in favor of holding new parliamentary elections.
Viktor Yanukovych, the leader of the party, may feel he has a chance now to win a majority in parliament.
But this could be wishful thinking. The chances are that new parliamentary elections would merely confirm the divisions that so badly rift Ukraine, further alienate the country's long-suffering electorate, and do nothing to bring political compromise any closer.
President Yushchenko is postponing any decision on what to do next by calling on parliament to elect a new constitutional court before he nominates anyone for the position of prime minister.
He has also said that any new prime minister must be a moderate with no "business interests." He clearly wants to exclude Yanukovych but may have in mind Renat Akhmetov as a compromise candidate. He is the richest and one of the most influential members of the Party of Regions.
As the political battles in parliament continue, the government appears rudderless. In the meantime, negotiations have resumed to create an international gas consortium to manage the Ukrainian gas pipeline system. This consortium would most likely consist of Ukraine, Russia, and Germany.
Russia, which earlier this month threatened to increase the price of gas for Ukraine, has apparently decided to wait and see. It may fear that a significant increase in the gas price would show that the pro-Russian Party of Regions is no more able to influence decisions made in Moscow than Yushchenko.
Lacking Central Government
In the absence too of strong central government, regional and city councils in eastern Ukraine are challenging the authority of the state. They have refused to obey orders to rescind resolutions making Russian the "second official language" -- resolutions that are in direct contradiction of the constitution.
Yushchenko appears either unable or unwilling to use force to enforce the law and is in danger of losing face with his core support in Western Ukraine. Many there are demanding that he act forcibly to prevent the country from sliding into anarchy.
But, as Yushchenko no doubt fears, a show of force may make matters worse.
Campaign stands on a Kyiv street in ahead of the March 26 elections (RFE/RL)
RELOADED DEMOCRACY: On March 16, Ukrainian Ambassador to the United States OLEH SHAMSHUR held a briefing at RFE/RL's Washington office. Shamshur discussed the political and economic achievements of the last year and the political environment in the run-up to the legislative elections. "Many people would say it was a year lost," he said. "And I would categorically, even definitely, object to that. I think that it was a year not lost; it was a difficult year; it was the learning period when we were learning, or in some instances, relearning to act under the democratic rules and procedures. Some mistakes which were made were avoidable, some were hardly avoidable, but in any case it was very important period for Ukraine as a country, Ukraine as a new, or if you wish, rediscovered, reloaded democracy."
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Click on the image for background and archived articles about Ukraine's March 26 elections.
Click on the image to see RFE/RL's coverage of the Ukrainian elections in Ukrainian.