President Hosni Mubarak will make an "important speech" at the end of a day when a quarter-million people turned out in the largest protest yet to demand his ouster. A visiting envoy of President Barack Obama told Mubarak Tuesday that the U.S. sees his presidency at an end, an administration official said.

It will be Mubarak's second speech since the biggest challenge to his nearly 30-year-rule began eight days ago. In the first, early Saturday, he named a vice-president for the first time who is widely considered his designated successor, sacked his Cabinet and promised economic and political reforms demanded by the protesters.

However, the throngs who have been protesting day after day say they will accept nothing short of Mubarak's departure.