Hundreds of Egyptian and Libyan protesters held up pictures of Gaddafi and ousted Egyptian President Hosni Mubarak, both with their faces crossed out.
Over a loudspeaker, one demonstrator said the Libyan protesters would break into the building and hold a sit-in unless the head of the consulate resigned.
"Resign and join the honourable diplomats who have turned against the killer Gaddafi or else the Libyan youth will break into the consulate and stage a sit-in," the protester shouted.
"We will not destroy or hurt anyone or anything but we will sit in until they resign."
Libyan diplomats at the United Nations and in several countries have broken ranks with Gaddafi, urging foreign countries to help stop what many called the slaughter of anti-government protesters.
Gaddafi's forces have cracked down fiercely on demonstrators demanding an end to his 41-year-old rule, with fighting spreading to the capital, Tripoli, after erupting in the oil-producing east last week.
Human rights groups say at least 233 people have been killed.
"Save the people of Libya from the bloodshed," the protesters chanted, with many women in the crowd weeping. "Stop the murderer, stop the killer, stop the massacre."
On Monday, hundreds had gathered outside the Libyan embassy in Cairo.
"I am here to show my rejection of the genocide that Gaddafi and his sons are launching against unarmed Libyans," said Egyptian professor Ali Barakat, 63, who was among those demonstrating in Alexandria.
"I am here to condemn international silence over these crimes that the world is watching on air," he told Reuters.