Egypt's political crisis deepened after tens of thousands of protesters in Tahrir Square demanded the country's top general step down and rejected an offer by the ruling military council to speed up the transition to civilian rule.

Demonstrations and clashes continued in several cities Wednesday, with one man shot dead by security forces in the northern port city of Alexandria. Police have denied using live ammunition, but most of the 30 people killed nationwide during the latest unrest have suffered bullet wounds.

The head of the Supreme Council of the Armed Forces, Mohamed Tantawi, vowed in a rare public address Tuesday to hold presidential elections by July 2012 and suggested he is willing to hold a referendum on whether military rule should end earlier.

The proposal is seen by many as a ploy designed to appeal to the many Egyptians who fear further upheaval and to divide them from youth activists.

Tantawi's speech followed crisis talks with political and Islamist groups, including the Muslim Brotherhood, which is expected to win a major share of parliament in staggered elections scheduled to begin Monday. Most liberal and secular opposition parties – who have called on the military to immediately cede power – declined to attend the meeting. They accuse the Brotherhood of selling out the revolution for short-term political gain.

Egypt's parliamentary elections have been hastily organized by the military. While Tantawi pledged Tuesday that the polls would go forward as planned, many opposition leaders believe that to be increasingly doubtful.

Tantawi also told the nation Tuesday he had accepted the resignation of the civilian Cabinet of Prime Minister Essam Sharaf, but that it will remain in place until a new government is formed.

Protesters vowed not to leave Cairo's Tahrir Square until the military council steps down. Clashes between police and demonstrators angry at Tantawi's speech erupted in several other cities, including Alexandria, Suez and Ismailiya.

In Washington, the U.S. State Department condemned “the excessive use of force by police” and urged restraint.

In an apparent concession to demonstrators, the military council earlier issued a law that bans anyone convicted of corruption from running for office or holding a government position. The move could restrict members of ex-president Hosni Mubarak's former ruling party from competing in the upcoming elections.

Amnesty International on Tuesday accused Egypt's rulers of brutality sometimes exceeding that of Mr. Mubarak.