Lawmakers approved changes to electoral law that are designed to prevent fraud, in return for reforms to the constitution that pass some presidential powers to parliament.
Davis said he's pleased Ukraine's parliament reached the compromise deal.
"I'm very pleased that the parliament of Ukraine has risen to this occasion," he said. "It's a vindication of what I've been saying for some time as secretary-general of the Council of Europe. I have been saying hat this is a problem to be solved by the Ukrainians, by the representatives of the Ukrainian people in combination, of course, with the Supreme Court. It's not for me to comment on the details of the agreement because it's a matter for the Ukrainian people and their representatives. But it does show the political maturity of Ukrainians, in that they have achieved an agreement."
Along with other international organizations, the Council of Europe had criticized the handling of the election's first two rounds, as well as strong media bias favoring the government's candidate, Prime Minister Viktor Yanukovych.
"We were very disappointed at the Council of Europe when we read the reports about the irregularities, reports that we received from our representatives who watched the elections, the observers," Davis said. "We were disappointed that more was not done between the first round and the second round to deal with the criticisms. We were disappointed with the media coverage, which, frankly, I think was very biased towards one candidate."
Charges of fraud brought out thousands of supporters of opposition candidate Viktor Yushchenko, who argued the results had been rigged to give victory to his rival.
The Supreme Court agreed and threw out the second-round vote on 3 December.
International mediators then held more talks in Kyiv to help end a deadlock over political reforms.
Those talks did not appear to include the Council of Europe. But Davis said the council was represented -- by Polish President Aleksander Kwasniewski. That's because Poland currently holds the rotating chairmanship of the council's decision-making body, the Committee of Ministers.
And as of yesterday, a team of Council of Europe experts has been in Kyiv to help prepare for the repeat vote.
"I've sent two experts [to] Ukraine to offer help," Davis said. "One is an expert in election procedures. Another expert has gone at my request to Ukraine to give first-hand advice to the Ukrainian authorities on how to achieve independent, objective, impartial coverage of elections. There are many countries in Europe where this does happen, where even state-owned radio and television give a fair and unbiased report. He's there to help Ukrainians to do that. He will also be reporting on what actually happens, and I hope we see some improvement in the next two weeks."
Davis said the Council of Europe is there to help and to give advice, not to pass judgment.
"We're going in the spirit of helping the Ukrainian authorities," Davis said. "We're not going to condemn or criticize. Our role is to help the authorities of the countries that are members of the Council of Europe -- our job is to help them do better."
Some of Ukraine's civil servants returned to work today for the first time in more than two weeks after opposition supporters ended their blockade of some government buildings in Kyiv.
Yushchenko congratulated his supporters, saying they had won a "great victory."