Prime Minister Viktor Yanukovych suggested he may agree to take part in early parliamentary elections as demanded by his rival, President Viktor Yushchenko.
He said he could participate in the ballot even if the Constitutional Court rules against Yushchenko, provided all participants in the political process agree.
Yanukovych had previously said he would agree to the poll only if an early presidential election was held simultaneously.
Yanukovych and his allies have asked the Constitutional Court to examine the legality of Yushchenko's April 2 decree to dissolve parliament and call early elections.
In an interview with RFE/RL's Ukrainian Service on April 11, President Viktor Yushchenko said the only democratic way to resolve the political crisis in his country is by holding new elections.
But speaking today at a news conference in Kyiv, Yushchenko indicated he was prepared to allow for more time before the elections, slated for May 27.
Speaking to RFE/RL, Yushchenko assured that dialogue between all forces in the dispute is continuing.
"I think the difference is that we are constantly consulting. There is an active dialogue. We have a regular dialogue with all the institutions of power. There is no feeling of isolation on the part of the parliament, the government, or the presidency as far as communication or dialogue is concerned," Yushchenko said.
Ukraine's Constitutional Court is due to start hearings into the decree's legality on April 17, although five out of 18 judges are refusing to consider the case, citing political pressure.
Speaking at a press conference today, Yushchenko called on Constitutional Court judges to be courageous and said that a court decision was a matter of principle for 48 million Ukrainians.
Meanwhile, international diplomatic efforts to solve the crisis are under way.
Russian and Polish diplomats were in the capital to discuss with Ukrainian government officials ways of resolving the crisis.
And the European Parliament's vice president, Marek Siwiec, held a news conference in Brussels today following a fact-finding mission in the Ukrainian capital.
But Yushchenko said he is confident that Ukrainians could resolve the crisis "by themselves":
"We should settle these internal problems through political means. Ukrainians should go through this by themselves because this [experience] is not something that you can borrow from someone else or receive it as a gift from someone," Yushchenko said.
RFE/RL's Ukrainian Service asked people on the streets of Kyiv on April 11 whether the Constitutional Court will be able to determine the constitutionality of the president's decree dissolving parliament.
Oksana, a student from Lutsk:
"Their decision will at any rate be beneficial to one of the political forces."
Oleksandr, a high-school student:
"[The court] will be able to do it, but only if the judges agree upon it."
Alla Asilyevna, a pensioner:
"How can the Constitutional Court solve the problem if there is pressure on it from all sides?"
Ivan Yukhimovich, a pensioner:
"If [Prime Minister Viktor] Yanukovych and [President Viktor]Yushchenko find an agreement, everything will be resolved."
Yuliya, a worker:
"I doubt very much that the judges will agree on anything."
RFE/RL's coverage of Ukraine. The Ukrainian-language website of RFE/RL's Ukrainian Service.