The European Union says agreements on association and free trade with Ukraine could be in jeopardy if Yanukovich does not free former prime minister Tymoshenko, his fiercest opponent, who was jailed in 2011.
The EU says her trial for abuse of office was political.
With the signing of these agreements set for November, the Tymoshenko issue is coming to a head even as Russia, Ukraine's biggest single trading partner, piles pressure on Kiev to halt its drive towards Europe and join a Russia-led Customs Union.
In an attempt to end the deadlock over Tymoshenko, European envoys have sought to persuade Yanukovich to pardon her so she can go to Germany for treatment for chronic back trouble.
Replying to a question on Tymoshenko in a television interview on Friday, Yanukovich, however, said:
"Unfortunately, in Ukraine, nobody has such authority, including the president ... Our laws do not allow for such circumstances".
Hinting at possible changes to legislation, he said:
"The law would have to be changed so that someone would be provided with the authority to do this."
He said most political forces in parliament would "unite" to solve outstanding problems relating to European integration and he was optimistic that Kiev would meet criteria laid down by the EU for signing the agreements at a summit in Vilnius, Lithuania.
These so-called benchmarks for democratic progress relate to reforming the judiciary, ending politically motivated prosecutions and improving electoral legislation.
"Demands for the signing of association ... were put to Ukraine and we are working on them, putting the finishing touches, we might say. A final full-stop will be written this autumn. We will fulfill all the conditions. I have no doubt of this," he told 1+1 television channel.
But many diplomats say it is unlikely the agreements will be signed unless Yanukovich relaxes his stance on Tymoshenko.
Kiev has stuck to its aspiration of joining the European mainstream and turning away from its former Soviet master, but Yanukovich has not shown any inclination to free Tymoshenko.
She is his strongest political opponent and could doom his chances of re-election for a second term in 2015 if she became political active again.
Even as the Kiev government seeks to persuade the EU that Ukraine is a fit partner for the future, it has come under pressure to back-track from Russia, which fears a flood of highly competitive goods on the Russian market if Ukraine joins an EU free trade zone.
Prime Minister Mykola Azarov on Wednesday urged Moscow to accept the "reality" of a changing world after Russia conducted extra customs checks on Ukrainian imports in a warning shot to Kiev and Russia's Vladimir Putin spoke of possible "protective" measures by Moscow and its Customs Union allies.
The pressure has led to talk of a trade war in Kiev and injected new tension into Moscow's relationship with Ukraine, which has pleaded unsuccessfully for a lower price for strategic supplies of Russian gas to bring relief to its economy.
Yanukovich on Friday avoided blaming Putin personally for the tension, but spoke of Kremlin "hawks" who were pushing a tough line with Ukraine over its pro-Europe course.
But he again brought up the issue of costly Russian gas deliveries, saying that Ukraine was paying $130-150 per thousand cubic meters more than any other country under a contract with Moscow that was "unjust".
Russia, which would like control of Ukraine's gas pipeline network, has used the promise of much cheaper gas to try to coax Kiev into the Customs Union.
But rejecting Russia's entreaties, Yanukovich said:
"The proposals which have been made to us do not suit us. They are even humiliating for us. We are never going to go down that path. We will not trade up our country - that is our principle."
Source: Yahoo News