CAIRO — Mohamed ElBaradei, the Nobel Peace Prize laureate and former chief of the United Nations nuclear agency, said Wednesday that he intended to run for president, although he set conditions under which he would pursue the office vacated last month by Egypt’s longtime leader, Hosni Mubarak.

The announcement came amid a growing sense of uncertainty as Egypt begins to chart its future after decades of autocratic rule and as violence has begun to escalate.

On Tuesday night into early Wednesday, 13 people were killed and 140 wounded in fighting between Muslims and Christians in the suburbs of Cairo, the Health Ministry said. The clashes, which broke out during a protest by several hundred Christians over the burning last week of a church in the village of Soul, were a significant departure from the sense of solidarity that had prevailed among people of different backgrounds throughout the weeks of protests that led to Mr. Mubarak’s resignation.

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