* Yanukovich, back from meeting Putin, faces calls for change
* Opposition want him to cede control of government
* Russia links aid package to repayment of hefty gas bills
By Natalia Zinets and Richard Balmforth
KIEV, Feb 9 (Reuters) - Ukrainian protesters, now in their third month of action, kept up pressure on President Viktor Yanukovich on Sunday with a mass rally where opposition leaders called for an end to his "dictatorial" powers.
About 20,000 demonstrators rallied on Kiev's Independence Square, focal point of the protest movement, as Yanukovich searched for a new prime minister and the currency of the heavily indebted economy, the hryvnia, remained under strain.
Russia piled further pressure on him at the weekend, linking disbursement of the next tranche of its $15 billion aid package for Kiev to repayment of a hefty gas bill owed to Russian firms.
Opposition speakers addressed both Yanukovich's governing style and his decision to seek closer economic ties to Russia rather than sign a free trade pact with the European Union.
"We want the system changed in the country - we want a system in which the president serves the will of the people, a president who does not have dictatorial powers," former economy minister Arseny Yatsenyuk told the crowd.
Far-right nationalist Oleh Tyahnibok attacked Russia's influence over Yanukovich, declaring: "Our struggle is not only against the regime of Yanukovich, but against those who support them - against the Kremlin's imperialistic policy."
Yanukovich met Russian President Vladimir Putin on the sidelines of the Sochi Winter Olympics on Friday. ID:nL5N0LD03T]
He has since returned to Kiev but no word has yet filtered out on what the two men discussed.
In an unusual move, the state security service placed anti-terrorism units on alert in what it called a preventive step to stop possible attacks on sensitive installations such as airports and power stations.
It said the new measures would apply to the blocking of approaches to state buildings and calls to seize installations where weapons are stored, a possible move against some radical protesters who have been in violent clashes with police.
The daily protests have complicated Yanukovich's search for a new prime minister to replace Mykola Azarov, who stepped down on Jan. 28. Choosing one unacceptable to the protest movement - could lead to an explosion of anger on the streets.
Yanukovich sparked the protests last November by choosing the $15 billion lifeline from Moscow for Ukraine's ailing economy rather than the EU link that millions of Ukrainians see as their country's future.
At least six people have died in occasional violent clashes between radicals and riot police.
Opposition leaders, with the backing of the Western powers, are pressing for constitutional changes that would re-balance powers - now heavily weighted towards the presidency - between the president, government and parliament.
They have already turned down offers of government posts under Yanukovich and are seeking instead to lead a technocrat government independent of him to manage the ailing economy.
OUTSTANDING GAS BILLS
Vitaly Klitschko, another opposition leader, accused Yanukovich of stalling in talks with them.
"He says we can change the constitution but that we have to wait months. People are not prepared to wait half a year," the boxer-turned politician told the crowd. "They want one thing - early presidential elections."
The next presidential election is due in early 2015.
With the United States and its European allies pressing for Yanukovich to change his mind, Russia has frozen further disbursements under a $15 billion aid package of credits and cheaper gas until it sees the colour of Kiev's next government.
Russian Finance Minister Anton Siluanov has also pointedly reminded Kiev of its gas debt of $2.7 billion to Moscow.
"We will fulfil what we have promised to Ukraine, but we would like the Ukrainian side to comply with the obligations that it has committed to," he said on Satuday. (Writing By Richard Balmforth; Editing by Tom Heneghan)