The last public comments by Tymoshenko had been on Sunday night after the publication of exit polls.
Yanukovych has twice called on Tymoshenko to resign her post as prime minister, but a senior aide on Thursday said her government had no intention of stepping down.
Borys Kolesnikov, Yanukovych's election campaign manager, said earlier that if Tymoshenko did not resign, she would be dismissed and a new prime minister would be found.
If Yanukovych was unable to form a coalition in parliament, he would have to call a snap parliamentary election.
Ukraine's central election commission said on Wednesday that Yanukovych had won 48.95 per cent of the vote in the pesidential poll, compared to Tymoshenko's 45.47 per cent.
Although official, the results are still preliminary and must be formally certified by the commission this month.
Tymoshenko's team has claimed widespread violations took place during voting, particularly in Yanukovych's eastern Ukraine strongholds, but international observers hailed the vote as a fair and clean.
The political standoff threatens to cause further disruption to the government which has repeatedly been paralysed by infighting.
It could also delay the resumption of International Monetary Fund lending which last year was crucial for the state's finances but was suspended because of broken promises of fiscal restraint.