About 70,000 pro-Western Ukrainians have gathered in central Kiev, promising never to abandon their drive to oust President Viktor Yanukovich over his alliance with Russia.
Opposition leaders took to a podium on Independence Square on Sunday to increase pressure on Yanukovich to appoint a new pro-Western government.
"None of the kidnappings and tortures have yielded any results," Igor Lutsenko told AFP news agency.
In a statement on Sunday, the country's security agency warned of a "heightened risk of terrorism", and put its counter-terrorism units on alert after receiving a large number of bomb threats at airports, train stations, pipelines and other locations across the former Soviet nation.
Al Jazeera's Neave Barker, reporting from Kiev, said that the alert was an unusual step by the Ukranian authorities.
The rhetoric of the protesters has changed from EU integration to get Yanukovich to step down, said our correspondent.
The country of 46 million people has been in chaos since November, when Yanukovich rejected a trade deal with the EU in favour of closer ties with Russia, stunning pro-EU parts of the population and sparking violent protests.
Since then, what started out as a localised, domestic period of unrest has snowballed into a struggle for Ukraine's future between Russia and the West, as demonstrations continue and spread to other parts of the country.
Yanukovich has already yielded to some opposition demands by dismissing the government, but he also has to appease Russia, which has effectively frozen a much-needed $15bn bailout until the situation improves.
The embattled Ukrainian leader held talks with President Vladimir Putin on Friday in the Black Sea resort of Sochi.
It is unclear what the two discussed, but Yanukovich had been expected to raise the issue of the bailout, of which Russia has so far issued only one instalment of $3bn.
Putin's bailout would reduce the future price of Russian gas imports by a third.
But Russia's Economy Minister Anton Siluanov warned on Saturday that Moscow would need at least a partial down payment on an outstanding $3.3bn gas bill before the terms of its Ukrainian package were restored.