Witnesses said that Mr Abbas' forces fired into the air to disperse the crowd of thousands after mourners began throwing stones at the security officers.
Medical workers said the man was shot in the neck and several others were wounded. Dozens were arrested and security officers confiscated the flags of Islamist groups including Hamas, witnesses said.
The crowd gathered for the funeral of a demonstrator killed on Tuesday (local time) at a rally held by a small Islamist group against the US-sponsored Annapolis peace conference.
Witnesses at the rally said the man was shot by security forces but police denied responsibility.
Mr Abbas agreed with US President George W Bush and Israeli Prime Minister Ehud Olmert at Annapolis to launch immediate talks on creating a Palestinian state alongside Israel with, a goal of sealing an accord by the end of next year.
Mr Abbas, who lost control of the Gaza Strip to Hamas Islamists in June, holds sway in the Israeli-occupied West Bank and has promised to crack down on militants as part of a 2003 US "road map" peace plan. © 2007 Australian Broadcasting Corporation