Viktor Yanukovych (search) vowed to fight on for Ukraine's presidency, despite handing the opposition of this ex-Soviet Republic a begrudging victory by announcing his resignation as prime minister.

His opponent, Western-leaning opposition leader Viktor Yushchenko (search), soundly won last weekend's court-ordered presidential revote, but Yanukovych has refused to concede, vowing to challenge the results in the Supreme Court. Under Ukrainian election law, Yushchenko cannot be declared president until all appeals against the voting are exhausted.

The pro-Russian Yanukovych announced his resignation as prime minister on Friday in a televised address, his first significant concession since losing Sunday's vote, but said he will maintain his claim to the presidency.

"I have made the decision to submit my formal resignation," Yanukovych told the nation.

"We are still fighting, but I don't have much hope," he said. "I will act as an independent politician, as the rightful winner of the legitimate Nov. 21 election."

Yanukovych was named the victor in that vote, but hundreds of thousands of Ukrainians flooded Kiev's streets to protest what they said was their stolen votes. After weeks of protests, dubbed the "Orange Revolution" after Yushchenko's campaign color, the Supreme Court ruled that the election had been corrupted by mass fraud, annulled Yanukovych's victory and ordered Sunday's revote.

Later Friday, outgoing President Leonid Kuchma told the nation in a separate televised address that "in 2005, there will be a new president. Every region and every citizen of Ukraine must accept this democratic choice as their own because this person will need your support."

Kuchma didn't mention Yanukovych's resignation in his speech.

Yanukovych, appointed prime minister in 2002, has seen much of his support fall away, losing the backing of Kuchma as well as many of his top advisers. Parliament passed a vote of no-confidence in his government Dec. 1, but he called it illegal.

When he returned this week after taking a leave from office to campaign, the opposition blockaded Yanukovych's government headquarters, refusing to let him convene a Cabinet session. The meeting went ahead in another building without him.

"I believe it is impossible to have any position in a state that is ruled by such officials," he said, in an apparent reference to Kuchma.

His resignation triggers the immediate resignation of the 20-member Cabinet. According to the constitution, Kuchma must accept Yanukovych's resignation and appoint a new government within 60 days — though he is likely to appoint a caretaker until the new president is inaugurated.

Yuriy Kliuchkovskiy, a lawmaker and Yushchenko ally, called Yanukovych's decision an acknowledgment that his position is "hopeless."

"There is his pride. He didn't want to submit his resignation documents to newly elected President Yushchenko, he decided to submit them to President Kuchma," he said.

Meanwhile, Yushchenko and Georgian President Mikhail Saakashvili welcomed the New Year side by side on Kiev's Independence Square, the epicenter of mass protests that overturned the political order in this nation of 48 million.

Saakashvili catapulted to power last year in a bloodless revolution that inspired the Ukrainian opposition. The joint appearance of two post-Soviet politicians who have openly and actively courted the West is certain to further irk the Kremlin, which had strongly supported Yanukovych.

"I couldn't support you as an official during your revolution, but I was with you and I feel myself again a resident of Kiev," Saakashvili, who studied international law in the Ukrainian capital, told the crowd in Ukrainian.

Saakashvili later joined Yushchenko on Independence Square, telling tens of thousands that "on this square, the future of Europe is being resolved."

The bitterly fought presidential race in Ukraine increased tensions between the West and Russia, which has accused foreign states of meddling in Ukrainian affairs.

Some Russian politicians also have accused the United States of being behind the U.S.-educated Saakashvili's rise to power. The Kremlin's relationship with Tbilisi has worsened under Saakashvili, who has aimed to boost Georgia's ties with the European Union and the United States.

Yushchenko has pledged to nudge Ukraine closer to the West, making it a priority to pursue a future EU membership.