The European Union wants Mr Yanukovich to free former prime minister Ms Tymoshenko, who was jailed in 2011 for abuse of office after a trial that it says was politically motivated. The EU has warned key association agreements due to be signed in November could be in jeopardy.
As a compromise, envoys from the European parliament have sought to persuade the president to pardon Ms Tymoshenko and let her go to Germany for treatment for chronic back trouble.
But Mr Yanukovich said yesterday: "Our laws do not allow for such circumstances. The law would have to be changed so someone would be provided with the authority to do this.
"Unfortunately, in Ukraine nobody has such authority, including the President."
Mr Yanukovich, whose country is facing trade pressure from Russia over its drive for European integration, said nonetheless he was sure Ukraine would meet criteria laid down by the EU for the signing of association and free trade agreements at a summit in Vilnius, Lithuania, in November.
These so-called benchmarks for democratic progress relate to reforming the judiciary, ending politically-motivated prosecutions and improving electoral legislation.
He said: "Demands for the signing of association were put to Ukraine and we are working on them, putting the finishing touches.
"A final full-stop will be written this autumn. We will fulfil all the conditions. I have no doubt of this."