UPDATE 3-Obama to reach out to Muslims in Egypt speech

* Obama seeks to restore links damaged under Bush

* June 4 Speech in Egypt will fulfill campaign promise

* Mubarak to visit Washington this month

* Obama urged to address human rights in Muslim world (Updates with Amnesty International reaction)

By Ross Colvin

WASHINGTON, May 8 (Reuters) - U.S. President Barack Obama will deliver a much anticipated speech to the Muslim world in Egypt next month, seeking to repair ties that were severely damaged under his predecessor George W. Bush.

Many Arab and Muslim nations were angered by the invasions of Afghanistan and Iraq, harsh interrogation of terrorism suspects at Guantanamo, abuse of prisoners in Iraq and Bush's initial reluctance to pursue Israeli-Palestinian peace.

Obama's Egypt trip fulfills a promise he made during his presidential campaign to give a major address to Muslims from a Muslim capital during the first few months in office.

The Muslim world will be watching to see his approach to the Israeli-Palestinian conflict. Most Muslims believed Bush's policies toward the region were biased in favor of Israel.