The effort is spearheaded by Javier Solana, the EU's foreign and security policy coordinator. Among others, the presidents of neighboring Poland and Lithuania have announced visits to Kyiv.
Solana said earlier this week he was in phone contact with opposition candidate Viktor Yushchenko, who has rejected the official election results, as well as with Prime Minister Viktor Yanukovych and incumbent President Leonid Kuchma.
Arriving in Kyiv today, Solana said he expects to have face-to-face meetings with all three. He repeated that the EU view is that the second round of the presidential election did not meet international standards of democracy. However, Solana also stressed the need to restore unity in the country.
"We are concerned about the [election] process. We don't think the process has been properly done, but we would like to see if that can be repaired and to [restore] the unity of the country and move the country forward," Solana said.
However, there appears to be some uncertainty in Brussels as to how the EU mediation effort is coordinated.
Formally, such contacts are run by what is known as the EU "troika" -- Solana, the current presidency, now held by the Netherlands, and the external affairs commissioner. A Dutch envoy was in Ukraine yesterday and, apart from Solana, the presidents of Poland -- an important regional player -- and Lithuania are also seeking to influence events.
There appears to be little contact between the EU envoys and the U.S. administration, which has also vocally condemned the elections. One EU official told RFE/RL today that while the bloc and the United States "share their analysis" of the situation, the EU is involved in Ukraine on its own terms.
Officials in Brussels have declined to reveal details of the talks. Emma Udwin, a commission spokeswoman, suggested today that the EU might consider offering unspecified "political" incentives to Ukraine.
"It is encouraging to see a readiness to think new thoughts, as I say, about both the European political structure itself and the way out of this particular impasse. I don't think it would be helpful of me to go into details at this stage," Udwin said.
At the same time, Udwin rejected suggestions that the EU may offer extra financial aid to Ukraine.
The EU has welcomed a decision by the Ukrainian Supreme Court to delay the official publication of the election results announced on 24 November by the country's election commission until complaints lodged by Yushchenko supporters have been reviewed.
Udwin said the EU expects the courts will address the numerous irregularities noted by international observers.
"What we want to see is all irregularities and all complaints about the conduct, particularly about the second round of the Ukrainian elections, investigated, and corrected," Udwin said.
Dutch Foreign Minister Bernard Bot yesterday indicated that the EU would not accept a legal judgment brushing aside reports of irregularities.
Udwin also downplayed the significance of yesterday's postsummit public spat over Ukraine between Russian President Vladimir Putin and EU leaders. She said both the EU and Russia have "different points of departure" vis-a-vis Ukraine, but that does not amount to a power struggle.
"Ukraine does not have to choose between the EU and Russia. It is a significant partner for both the EU and Russia and we are not trying to pull or push Ukraine. It is simply, objectively, the case that both the EU and Russia have interests in this relationship and have influence in this relationship," Udwin said.
Solana, however, has noted that while the EU is concerned with the quality of democracy in Ukraine, Russia's main goal is to secure a particular outcome there -- the emergence of Yanukovych as the winner.
For his part, Russian Foreign Minister Sergei Ivanov chided the EU in Moscow today for what he called its meddling in Ukraine's domestic affairs.