BERLIN, Sept 1 (Reuters) - The Alternative for Germany (AfD) was on track to become the first far-right party to win a regional election in Germany since World War Two, projections showed, giving it unprecedented power even if other parties are sure to exclude it from office.

The AfD was set to win 33.2% of the vote in the state of Thuringia, comfortably ahead of the conservatives' 23.6%, broadcaster ZDF's projection showed on Sunday, a vote share that, depending on final seat allocations, could let it block decisions requiring a two-thirds majority.

The appointment of judges or top security officials are among such decisions. If the AfD, led in Thuringia by Bjoern Hoecke - its most extreme and controversial figure - decides to block them, it could weaken an apparatus, built up painstakingly over decades, designed to police and disrupt far-right forces.

In neighbouring Saxony, projections put the conservatives, who have run the state since 1990, on 31.5%, just 1.1 percentage points ahead of the AfD.

Conservative state premier Michael Kretschmer, who hailed the result as a success and a mandate to form a new government, blamed the strength of the far right on Social Democrat Chancellor Olaf Scholz's fractious coalition in Berlin.

"There is a huge lack of trust in politics that has to end," he said. "We need another political style in Berlin."

With a year to go until Germany's national election, the results are punishing for Scholz's coalition. All three ruling parties lost votes, with only his SPD comfortably clearing the 5% threshold needed to stay in parliament.

The anti-immigration AfD may have drawn momentum in the final week of the election from a deadly knife attack at a festival in the western city of Solingen, allegedly by an illegally resident Syrian national whom authorities had failed to deport.

"This is a requiem for the coalition," said the AfD's joint leader Alice Weidel. "The coalition should ask itself whether it can continue to govern at all."

The left populist Sahra Wagenknecht Alliance (BSW), which like the AfD wants less immigration and an end to arming Ukraine, came third in both states just eight months after its founding.

With all parties having ruled out working with the AfD, the BSW could be crucial to forming a stable government in the two states, which lag western Germany economically more than three decades after reunification.

Sahra Wagenknecht said her party hoped to form a government with the conservatives and other parties in Thuringia but would insist on a different approach to Ukraine - even though that lies far outside a regional government's competence.

The disastrous result for Scholz's coalition could further stoke conflict within it as all three parties seek to reassert their identity ahead of next year's national election.

For Weidel, her party's strong performance in both states was evidence that it was no longer possible to keep her party out of power.

"The voters want the AfD in government", she said. "Without us, a stable government is not possible."

Bodo Ramelow, the premier of Thuringia, whose Left party was battered despite his personal popularity, said all democratic parties now had to work together.

"I am not fighting the conservatives. I am not fighting the BSW. I am fighting the normalisation of fascism," he said.

Photo from Reuters