* Israeli PM lets parade go ahead as planned
* Palestinian factions warned march could spark conflict
* Jews visit Al-Aqsa compound, Palestinians fight police (Recasts as march gets under way)
By Crispian Balmer and Amar Awad
JERUSALEM, May 29 (Reuters) - Thousands of flag-waving Israeli nationalists marched through the Muslim quarter of Jerusalem's Old City on Sunday in a deeply divisive parade that Palestinian factions warned could re-ignite their conflict with Israel.
Police earlier fired stun grenades at Palestinians who pelted them with stones in the Al-Aqsa mosque compound as record numbers of Jews visited the holy site, some of them appearing to pray in defiance of a long-standing ban.
The annual Jerusalem procession celebrates Israel's capture of the Old City in the 1967 Middle East war and draws thousands of cheering, chanting participants to its narrow, stone streets.
"Death to Arabs," some youths shouted as they entered Damascus Gate, the main entrance to the Old City's Muslim neighbourhood. "An Arab is a son of a whore," one small group yelled out in front of Jerusalem's ancient walls.
Ahead of the march, police said 2,600 Jews toured Al-Aqsa esplanade, a record number for a single day. Some of the visitors wore religious garb and prostrated themselves. A few held up Israeli flags and sang the national anthem.
The preacher of the mosque, Sheikh Ikrima Sabri, denounced their behaviour. "What happened today in Al-Aqsa mosque hadn't taken place since 1967," he told Reuters, accusing the government of deliberately looking to escalate tensions.
The Islamist group Hamas, which governs the Gaza Strip, also condemned the scenes, which went viral on social media.
"The Israel government is fully responsible for all these reckless policies and the following consequences," senior Hamas official Bassem Naim told Reuters.
In recent years, Hamas has cast itself as a defender of Muslim Jerusalem. After weeks of confrontations last year over Palestinian evictions in the city, Hamas fired rockets into Israel during the march, triggering an 11-day war that killed at least 250 Palestinians in Gaza and 13 people in Israel.
DRONE
As nationalists draped in Israel's blue and white flag gathered at Damascus Gate, a drone flew overhead trailing a Palestinian flag. A man rushed up to the crowds and waved another Palestinian flag at them before being dragged away.
Inside the city, small fights sporadically broke out. One Israeli youth was videoed using pepper spray on a Palestinian woman, leading to an exchange of punches and kicks. However, some marchers said they had come in peace.