JERUSALEM, May 20 (Reuters) - Right-wing Israeli marchers scuffled with Palestinians as a procession marking the Jewish state's capture of east Jerusalem entered the old city's Muslim quarter on Sunday, police said.

Tens of thousands of Israelis turned out to celebrate the anniversary of the capture of the territory in a 1967 war.

Fifteen people were arrested after fighting between some marchers and Palestinians who gathered outside the Old City walls, said police.

"Ten Jews were arrested for calling out racist slurs and attacking Arabs. Five Arabs (were arrested) for throwing objects and attacking (Israelis)," Jerusalem's police force said in a statement.

Palestinians want east Jerusalem to be the capital of an independent state they hope to establish in the West Bank and the Gaza Strip. Israel considers the entire city its capital. Its annexation of east Jerusalem did not win international recognition.

"Israel without Jerusalem is like a body without a heart," Prime Minister Benjamin Netanyahu said at a commemoration ceremony on Sunday. "It will never be divided again."

Chief Palestinian negotiator Saeb Erekat condemned the celebrations, saying they were "clear proof that peace is not part of the Israeli government's agenda"