* Lithuanians reject austerity-focused government in ballot
* Three opposition parties aimed to form government
* President vetoes one of trio due to vote-rigging claims
* Economists say budget picture still tough
* PM candidate backs euro in 2015, better Russia ties
Lithuania's president vetoed plans on Monday by three opposition parties to form a government after a weekend election, saying claims of vote buying and tax fraud made one of them unfit to rule.
Voters turned against Prime Minister Andrius Kubilius' austerity-minded administration on Sunday, in a warning for other European governments pushing through tough budgets.
That put an alliance of the opposition Social Democratic Party, the Labour Party and the party of an impeached former president in prime position to succeed him.
But President Dalia Grybauskaite, a former EU budget commissioner who is popular with the electorate, refused to accept the Labour Party, which faces allegations of buying votes during the two rounds of balloting.
"A party which is suspected of gross violations in the election, which is suspected of false accounting and non-transparent activities cannot participate in the government's formation," Grybauskaite told a news conference.
The three opposition parties had said they would ease the pain of Kubilius' harsh budget cuts, which have forced many Lithuanians to emigrate in search of work.
The parties would also remain fiscally responsible, an approach that economists view as inevitable given Lithuania's high borrowing needs.
But the decision by Grybauskaite, whose task it is to name a prime minister, throws their plans into doubt.
She said she would eventually probably name Social Democrat Party leader Algirdas Butkevicius as prime minister, but insisted Labour should not be in the coalition.
"I will give support only to that political party which can form a majority without the Labour Party, which is sitting on bench of the accused," referring to the ongoing trial.
That could throw a lifeline to Kubilius, who has said he would not necessarily be against forming a rainbow coalition with Butkevicius.
Butkevicius, a former finance minister whose party will be biggest in parliament, told reporters he could not say now whether the Labour Party would be in his government or not.
If he wanted to avoid conflict with the president, he said he could form another coalition, or go into opposition.
He earlier told Reuters he aimed to take Lithania to the euro zone in 2015,
The president said police were investigating 27 election irregularities, of which 18 were alleged vote buying, with the Labour Party allegedly involved in most of them.
The party's leader Viktor Uspaskich is also on trial for alleged tax fraud at his party from 2004-2006, which he denies. The party increased its seats in parliament to 29 from 10.
"We call our state a democratic state, ruled by law," Uspaskich said on public television.
"The principle of the presumption of innocence must be kept to. The will of the people must not be spat upon," he added.
Kubilius won praise abroad for slashing the budget deficit after a brutal economic crisis four years ago.
The economy has returned to growth, and rose a faster-than-expected 4.4 percent in the third quarter.
But the outgoing premier saw his popularity slide at home as wages fell, unemployment rose and tens of thousands of people left the small Baltic country in search of work.
The opposition parties have said they would aim to increase the minimum wage, make the tax system fairer and boost investment.
Economists say a new government will have little room to ease back on the austerity as Lithuania needs to retain the confidence of debt markets.
The country needs to raise 7.6 billion litas ($2.85 billion) in 2013, about 6.5 percent of projected gross domestic product.
Butkevicius has said he would stick to the outgoing government's 2013 budget deficit target.