Morsi said Egypt did not interfere in the internal affairs of other countries, but that Syrians had "clearly" said they wanted change, al-Masry al-Youm reported.
Speaking in Cairo to foreign ministers of members of the Arab League, Morsi said "There is still an opportunity to stop the bloodshed."
He advised Assad, "Do not take the right decision at the wrong moment. There is no place for denial and one-upmanship. Do not listen to those who lure you to stay in power. The Syrian people have said clearly that they want change and not more wasted time on reform."
Morsi added, "Now is the time for change. There is still some time to stop the bloodshed. If you do not stop the bloodshed, it will all go down in history. We stand by the Syrian people to gain their full rights without interfering in their internal affairs."
Some 150 people died Wednesday in Syrian clashes as international aid groups and governments promised more aid to those affected by the conflict.
More than half of the casualties, 81, were reported from Damascus and the surrounding area, reported the Syrian Network for Human Rights. The organization said 18 people died in Syria's second-largest city, Aleppo, while another 14 were killed in Dier Alzoor and 10 in Hama.
The non-profit global health and disaster relief organization Americares said in a statement Wednesday donations of medicines and medical supplies had arrived in Jordan for 24,000 refugees at the newly-established Za'atri camp.
A previous shipment from Americares arrived Aug. 23.
The group said it is also supplying medical aid to volunteer doctors providing emergency medical care to refugees around the region.
The U.S, Agency for International Development said Wednesday it will give $21 million more to the World Food Program to provide food and other assistance to Syrians displaced by the ongoing conflict.
Dr. Rajiv Shah, the head of USAID, said the aid will help more than 780,000 people in Syria who have been driven from their homes by fighting between the regime and the rebel opposition. It also will be used to support the 240,000 Syrians who have fled to neighboring countries.
About 2.5 million Syrians are in urgent need of humanitarian assistance, the United Nations estimated in a separate statement.
Since the uprising began 18 months ago, the United Nations said more that 18,000 people, mostly civilians, have died.
On Tuesday, U.N. Secretary-General Ban Ki-moon called on member states to provide "strong and united support" for Lakhdar Brahimi, the newly appointed special representative for the United Nations and the League of Arab States on the Syrian crisis.
Brahimi assumes the post vacated by Kofi Annan in August.