"The country does not need another political crisis. The nation has spoken for a change in power and the prime minister should take the right decision and enter opposition."
Tymoshenko has disappeared from public view since making a short comment on Sunday after the release of exit polls and it was unclear when the usually talkative prime minister would reappear.
Her Bloc Yulia Tymoshenko party (BYuT) is reported to be split on the issue, with one faction seeking to persuade her to concede.
Sviatoslav Olyinyk, a deputy from the BYuT, said the prime minister could make a statement on Wednesday or Thursday recognising the election results.
But Sergiy Vlasenko, another BYuT deputy, said the party would ask for a recount in the eastern regions of Donetsk and Lugansk and in the Crimea peninsula, all Yanukovych strongholds where he polled extremely well.
The Interfax-Ukraine news agency said on Wednesday that a recount was already under way in one part of Crimea.
Olexander Turchynov, Tymoshenko's deputy, said the elections had been marred by violations.
"In the second round of the Ukrainian presidential elections, falsifications took place which had a substantial impact on the results and put in doubt the outcome of the vote," he said in a statement.
His comment is the highest-level reaction from her camp since the results were announced.
The conduct of Sunday's vote received ringing endorsements from Western election observers and governments who characterised it as free and democratic.
Ukraine's central election commission said on Wednesday that Yanukovych had won 48.95 per cent of the vote, compared to Tymoshenko's 45.47 per cent.
Though official, the results are still preliminary and must be formally certified by the commission this month.
In his first major foreign policy statement since the election, Yanukovych said on Wednesday that relations with Russia would be a key part of his presidency.
"A priority for us will be relations with Russia and the CIS," he said, referring to the Commonwealth of Independent States grouping of post-Soviet states.
"Our countries are closely linked by economics, culture and history."
Ukraine's relations with Russia deteriorated badly under Viktor Yushchenko, the pro-Western outgoing president, who rose to power in the country's Orange Revolution in 2004.
Dmitry Medvedev, the Russian president, has already congratulated Yanukovych on his victory.
A brief statement from the US embassy in Kiev praised the elections as a consolidation of democracy in Ukraine but made no mention of Yanukovych.