* Vote is first of three German regional elections this year
* National election follows in September
* Merkel's CDU conservatives remain the biggest party
* Neither the CDU nor left-leaning parties hold majority (Adds preliminary official results)
By Paul Carrel and Hakan Erdem
BERLIN/SAARBRUECKEN, Germany, March 26 (Reuters) - German Chancellor Angela Merkel's conservatives won a regional election in the western state of Saarland on Sunday, dealing a setback to their Social Democrat rivals and boosting her prospects of winning a fourth term in September's national election.
Merkel's Christian Democrats (CDU) strengthened their position as the largest party in the state despite expectations ahead of the vote that the Social Democrats (SPD) would be boosted by their new national leader, Martin Schulz.
The CDU won 40.7 percent of the vote, up from 35.2 percent in the previous election in Saarland in 2012, preliminary official figures showed. The SPD slipped to 29.6 percent, down from 30.6 percent.
Prior to the election, polls had indicated that a left-leaning "red-red-green" alliance of the SPD, the far-left Linke and the environmentalist Greens -- or even a "red-red" coalition if the Greens failed to win enough votes -- could emerge after the vote.
But the Greens failed to reach the 5 percent threshold required to enter the state assembly, while the SPD and Linke, which won 12.9 percent, lacked enough votes to form a coalition on their own.
"The people decided on stability and reliability," CDU Secretary General Peter Tauber said. "This result is a clear rejection of red-red-green."
Saarland has only 800,000 eligible voters, but the state election was the first of three regional votes ahead of the Sept. 24 federal vote and offered an opportunity for the parties to build, or lose, momentum for the national election.
Merkel has been an anchor of stability in Europe, which she has guided through the euro zone and migrant crises during her 11-year leadership, at a time when many voters are unnerved by rising populism.
The far-right Alternative for Germany (AfD), which bruised Merkel in regional elections last year after her decision in 2015 to open Germany's doors to migrants from the Middle East, won 6.2 percent of the vote in Saarland.
SCHULZ SETBACK
The dip in support for the SPD was a setback in its first electoral test under new leader Martin Schulz, whose promise to tackle inequality has resonated with many voters nationally and re-energised the centre-left party.
"This is a long-distance run, not a sprint," Schulz said with an eye on September's national election, but added that the outcome of Sunday's vote should not be "sugar-coated".