JERUSALEM, April 22 (Reuters) - Israel turned down on Sunday an offer by Pakistani President Pervez Musharraf to serve as a mediator in peace efforts with the Palestinians but said he would be welcome to visit the Jewish state. "There is a positive ongoing bilateral dialogue between Israel and the Palestinians. This dialogue will continue without the assistance of mediators," an official in Prime Minister Ehud Olmert's office said, referring to Musharraf's proposal. In remarks broadcast on Al Arabiya television on Saturday, Musharraf said he would be able to play a "big role" if he "was accepted as a neutral mediator by all sides". Like most Muslim countries, U.S.-allied Pakistan has no diplomatic relations with Israel, although senior officials from both countries have met on several occasions in recent years. Earlier this month, Olmert and Palestinian President Mahmoud Abbas began a series of confidence-building talks at Washington's behest. But Olmert said the dialogue would not include "final-status issues", such as borders and the future of Jerusalem and Palestinian refugees. Israel refuses to deal with the coalition government Abbas formed in March with the Islamist Hamas group. The movement has rejected Israeli and Western demands to recognise Israel, renounce violence and accept existing interim peace deals. The Israeli official, who declined to be identified, said Musharraf "is welcome to come and visit Israel, meet the Israeli leadership and hear the positions on the different issues". Israel, the official said, "would be happy to hear his position and advance the level of dialogue and of relations between Israel and Pakistan". (Additional reporting by Inal Ersan in Dubai)