Parties in the outgoing Slovak government began talks with the opposition on Wednesday to reach an early agreement on ratifying a plan to strengthen the euro zone's EFSF rescue fund.

Lawmakers rejected a plan to bolster the European Financial Stability Facility (EFSF) in a vote on Tuesday, toppling the center-right cabinet, but a second vote with opposition support is likely to approve the pact, possibly by the end of this week.

Slovakia, whose 5.4 million people make up less than 2 percent of the currency bloc's population and 1 percent of its total output, is the only member not to ratify the plan to boost the EFSF's powers and fight the spreading debt crisis.

Ratification by all 17 members is needed for the changes to take effect, and even as Slovak politicians wrangle over the July agreement, European leaders are mulling further steps that would protect euro zone banks if Greece defaults on its debts.

Germany and France, the leading powers in the bloc, have promised to propose a comprehensive strategy to fight the debt crisis at an EU summit on October 23.

Robert Fico, head of the Slovak leftist opposition party Smer, said on Tuesday he was ready for talks. His party supports the EFSF in principle but refused to support it on Tuesday because by abstaining it helped topple the government.

A spokesman for Prime Minister Iveta Radicova's Slovak Democratic and Christian Union (SDKU) said the party leaders would meet at an undisclosed location before a cabinet session due to start at 3 p.m. (1300 GMT). Media reported the meeting was under way at Parliament, but all parties declined to confirm that.

We want to vote on the EFSF as soon as possible, ideally on Thursday. Everything depends on whether an agreement with Smer is reached, SDKU spokesman Michal Lukac said.

Austrian Finance Minister Maria Feker said she had received a call from Slovak Finance Minister Ivan Miklos late on Tuesday and he had assured her there would be a quick deal.

He said he believed there will be an agreement with the opposition either tomorrow or Friday at the latest, she told Austrian radio.

Radicova's cabinet will remain in office until a new administration is formed. It will formally approve EFSF ratification again at the meeting and resubmit it to parliament, a government source told Reuters.

Parliament is next due to sit on Thursday afternoon, which would be its first opportunity to hold a new vote on the EFSF.

Tuesday's vote rattled global markets frustrated at the euro zone's inflexible decision making process at a time when Europe's debt crisis is worsening.

On Wednesday, world stocks slipped below an earlier three-week high, while top-rated government bonds rose as a weak start to the U.S. earnings season and the Slovak political crisis kept investors nervous.

DEAL SEEN QUICK

In Brussels, the presidents of the European Commission and the European Council urged a speedy resolution.

We call upon all parties in the Slovak Parliament to rise above the positioning of short term politics, and seize the next occasion to ensure a swift adoption of the new agreement, Commission President Jose Manuel Barroso and Council President Herman Van Rompuy said in a joint statement.

Radicova has asked SDKU leader Mikulas Dzurinda to lead the talks, which include two junior coalition partners. The fourth coalition member, Freedom and Solidarity (SaS), will not take part. Its opposition to EFSF ratification brought down the government in Tuesday's vote.

It refused to approve the deal because its leader, free-market ideologue Richard Sulik, argued that as the euro zone's second poorest members, Slovaks should not have to bail out higher-spending, richer countries like Greece.

Slovakia's portion of the 440 billion euros in guarantees backing up the EFSF would be just 7.7 billion, but Sulik had insisted this would be more than a fair share relative to Slovakia's economic output per head which is 74 percent of EU average, below Greece at 89 percent.

Many Slovaks fear that preventing the EFSF expansion could help exacerbate a new global downturn like the one that sent their economy from 10.5 percent growth in 2007 to an almost 5 percent contraction two years later.

Opinion polls show about 45 percent of Slovaks support the deal, versus 36 percent against.

It's embarrassing... I understand Sulik's arguments, and basically agree with them. But we don't live alone in a vacuum, rather we are in a society and we are responsible for it, said 43-year-old businessman Jan Repa.

President Ivan Gasparovic, responsible for appointing the next prime minister, cut short a visit to Asia to deal with the government collapse and was expected to return on Thursday.

Slovak politicians have several options. They can agree on a new cabinet, possibly with the support or even inclusion of Smer; they can agree to hold an early election; or they can name a caretaker government that would be backed by most political parties.

(Additional reporting by Petra Kovacova in Bratislava and Sylvia Westall in Vienna, writing by Jan Lopatka and Michael Winfrey; editing by Tim Pearce)