* German lawmaker has pushed for bigger role for EU Parliament
* Two-thirds of valid votes go to Social Democrat Schulz
* Schulz eyes tax reform, combating financial speculation (Adds Schulz comments, background)
BRUSSELS, July 1 (Reuters) - The European Parliament on Tuesday chose Martin Schulz as its president for another two and half years, backing a combative social democrat who has fought for more power for the EU legislature.
The extension of the German lawmaker's term follows the parliament's success in getting its candidate, Jean-Claude Juncker, nominated as European Commission President and shows lawmakers' determination to have a greater say in Europe.
"Today, no-one can get around the EU Parliament," said Schulz, a former bookstore manager from a small town near the German-Belgian border.
Of 612 valid votes cast in the parliament's seat in Strasbourg, 409 were for Schulz.
He told reporters he would focus on tackling issues including tax reform and financial market speculation. The new legislature will also have to ratify an ambitious free-trade deal between the European Union and the United States if negotiations between Brussels and Washington are successful.
Schulz said that the parliament's success in introducing a system of lead candidates from European political groups for EU elections in May marked a leap forward. Those changes resulted in Juncker's appointment as Commission president, despite the opposition of British Prime Minister David Cameron.
"The process is a major strengthening of the European Parliament," he said. "This is a process which will cause major changes in Europe."
The European Parliament's gain in authority comes at the expense of individual EU countries, which in the past had a free hand to set the course of legislation or decide policy in areas such as trade. That has changed since EU lawmakers gained more authority to influence legislation under reforms that came into effect in late 2009.
The son of a German policeman, Schulz - who former Italian prime minister Silvio Berlusconi once compared with a Nazi concentration camp guard - has been credited with cementing the European Parliament's new status.
Often deliberately over-staying his welcome at summit meetings with European Union leaders and credited with heightening the profile of recent European elections in Germany, Schulz now faces a challenge from protest parties that won seats in the parliament in the May vote.
Across the continent, parties of the far right and far left more than doubled their representation, buoyed by resentment with Brussels over immigration and record unemployment.
While the centre-right and centre-left will still control more than half the 751 seats in the EU legislature, they will face constant heckling from anti-EU lawmakers.
Speaking just before Schulz's reelection, European Council President Herman van Rompuy, who chairs the meetings of EU leaders, highlighted the challenge ahead.
"The eurosceptic parties have never been as strong as today," Van Rompuy told an event in Brussels. (Reporting by John O'Donnell; Editing by Robin Emmott, Larry King)