The call came as human rights groups said at least 28 people were killed by Syrian security forces in violence that erupted in Hama, Homs, Idlib and Deir al-Zour Tuesday.
The British group Syrian Observatory for Human Rights and the Local Coordinating Committee said they had documented the deaths of at least 28 civilians, The (Beirut) Daily Star reported Wednesday.
Syrian Observatory for Human Rights said in addition to the civilian deaths, five military deserters were killed.
The deaths occurred the same day the U.N. General Assembly's human rights committee condemned Syria for its bloody crackdown on anti-government protesters in a resolution backed by a number of Arab countries and the West.
The resolution passed by the committee condemned Syria for the "continued grave and systematic human rights violations by Syrian authorities."
In response to the non-binding resolution, Bashar Ja'afari, Syria's envoy to the United Nations, protested it would not benefit his country, and accused the United States of masterminding and instigating a political campaign against Syria, the Chinese news agency Xinhua said.
Turkish Prime Minister Recep Tayyip Erdogan Tuesday urged Assad to learn from history.
"It is not heroism to fight against your own people," Erdogan said in remarks delivered to his ruling Justice and Development Party but addressed to Assad.
"If you want to see someone who has fought against his own people, look at Nazi Germany, [German Nazi leader Adolf] Hitler, [Italian fascist leader Benito] Mussolini, [Nicolae] Ceausescu of Romania," Erdogan said. "If you do not learn your lesson from them, look at the Libyan leader, who pointed his gun against his own people and, only 32 days ago, got killed in a way that none of us desired, after using the same phrases that you use.
"Without spilling any more blood, without causing any more injustice, for the sake of peace for the people, the country and the region, finally step down.
"Leave your seat before you tyrannize any more," he said, becoming the second regional leader, following Jordan's King Abdullah last week, to call on Assad to quit.
Erdogan spoke a day after Syrian gunmen attacked a bus convoy carrying Turkish pilgrims home from Mecca, wounding two of them. Passengers said the attackers wore Syrian security force uniforms.
Earlier this month, pro-Assad demonstrators attacked Turkish diplomatic missions in Damascus, Aleppo and the port city of Latakia, burning Turkish flags and shattering windows.
Turkey is hosting an armed opposition group of Assad-regime army defectors waging an insurgency against Assad, providing shelter to the commander and dozens of members of the group, known as the Free Syrian Army. It is also letting them orchestrate attacks across the border from inside a camp guarded by the Turkish military.
Turkey said it also reserved the right to impose a buffer zone within Syria to protect civilians if it experiences a flood of refugees from Syria into Turkey.
The two countries were once close allies.
Last week the Arab League voted to suspend Syria and warned harsh sanctions would be imposed if Assad continued to violate efforts to restore calm to the area.