Former Ukrainian Prime Minister, Yulia Tymoshenko, a leading opposition figure, has been on trial since June for abuse of office over a gas deal signed with Russia in 2009. She could face up to 10 years jail if convicted.
The Yanukovich administration says the deal left Ukraine paying an exorbitant price for Russian gas supplies. Tymoshenko who, denies the charge, says her trial is a political vendetta.
The United States and EU members have largely taken her part. Some EU members say the trial could block an agreement on closer ties and easier trader with the ex-Soviet republic.
When the hearing re-convened on Monday in Kiev, the court judge announced an adjournment until 27 September "to guarantee the rights of the defence and provide extra time".
In Brussels, a spokesman for EU foreign affairs chief Catherine Ashton said she and US Secretary of State Hillary Clinton wrote to Yanukovich on Friday. "It (the letter) was private in nature," said spokesman Michael Mann.
But a Brussels-based diplomat familiar with the text said: "I think it's fair to say the letter expresses concern about the state of democracy in Ukraine and refers specifically to the arrest and detention of Tymoshenko, which is troubling."
The source said the EU and the United States had expressed their commitment to help Ukraine build a strong and prosperous democracy, in which the rule of law is paramount.
"It (the letter) talks about concerns about politically motivated trials in general, and says that such actions can harm Yanukovich's reputation," the source said, adding that the letter urged him and his government to intervene with courts.
The adjournment on Monday by Judge Rodion Kireyev caught the prosecution and the defence team off balance. Tymoshenko herself had said she expected sentence to be passed this week.
"We were surprised. We were ready for today's hearing," prosecutor Liliya Frolova told Reuters.
Tymoshenko, 50, who narrowly lost to Yanukovich in a bitter fight for the presidency in February 2010, said: "This shows that the case has unravelled."
Yanukovich himself left Kiev on a two-day visit to Turkmenistan and his spokesmen were not available for comment.
Ashton is due to visit Kiev at the end of the month to discuss prospects for an association agreement between the bloc and Ukraine, including creation of a free trade zone.
The trial has polarised politics. Hundreds of Tymoshenko's supporters have camped out overnight on Kiev's main thoroughfare throughout the summer to demonstrate solidarity. They say Yanukovich ordered the trial to neutralise her as a political figure ahead of a parliamentary election in October next year.
But many commentators say the trial has turned out to be a public relations disaster for him, bringing not only criticism from the West but also from Russia, with which Yanukovich's government is trying to negotiate a new price for gas.
Tymoshenko, a fiery speaker who led thousands of protesters during the 2004 "Orange Revolution" that sank Yanukovich's first bid for the presidency, had been in slow decline politically. But the trial and her subsequent detention, ordered by the judge for contempt of court, has resurrected her as a major force.