Meanwhile, the United Nations said some 450,000 people are now believed to have fled their homes as a result of the post-election crisis, which African leaders will discuss again on Wednesday at the African Union headquarters.
Demonstrations were held in various parts of Ivory Coast's main city, a week after Gbagbo's forces shot dead seven women at an all-female march in Abobo, a neighbourhood that has backed Alassane Ouattara, Gbagbo's rival.
Though these ones appeared to go more peacefully, they were swiftly followed by outbreaks of gunfire in many of the neighbourhoods where they happened.
In Port Bouet, near Abidjan's airport, witnesses said about 50 pro-Gbagbo youths armed with AK47 assault rifles and machetes turned up to disperse 200 women who tried to march there.
"They fired into the air to disperse the women. They had weapons to intimidate them, but they didn't hurt anyone," said Bernard Aurega, vice president of Ouattara's party in Port Bouet, who saw the march.
Ever since Gbagbo rejected U.N.-certified results showing he lost a November presidential election to Ouattara, supporters of the latter have seen their attempts to protest being met generally with violent repression.
The poll was meant to end a decade of instability and economic stagnation but resulted in deadlock and rising violence in Abidjan and the west of Ivory Coast has raised the prospects of another civil war in the world's top cocoa producer.
The U.N. has said at least 365 people have been killed during the crisis but diplomats believe the real toll is much higher.
U.N. aid agencies have revised the figure for people displaced to about 450,000, including some 90,000 who have fled into neighbouring Liberia.
Ouattara's camp said he is due to attend a meeting at the AU headquarters in Ethiopia this week to discuss the crisis but pro-Gbagbo officials said he would send representatives.
Optimism for a diplomatic breakthrough is low.
Seven women were killed last Thursday after security forces opened fire on protesters in the northern pro-Ouattara suburb of Abobo, according to witnesses and military sources.
On Tuesday, a march there went off peacefully but was swiftly followed by bursts of gunfire.
"Gbagbo, assassin! Gbagbo, power thief! Leave!" the women shouted and sang, some in traditional dress, others wearing T-shirts printed with Ouattara's face.
The only men with guns present were pro-Ouattara youths with AK-47s and civilian clothes, who residents said were there to protect the march. One warned Reuters TV not to film them.
But witnesses said almost as soon as the march petered out, machinegun fire rocked the neighbourhood.
"We've been hearing machinegun fire for much of the afternoon. It sounds like two groups fighting each other but I don't know," said resident Tiemoko Souala.
Another Abobo resident said they saw security forces move along the main street before the machinegun fire erupted.
Abobo is now largely controlled by insurgents calling themselves the "invisible commandos" and professing loyalty to Ouattara, after a week of gun battles in which they pushed out police and military loyal to incumbent leader Gbagbo.
In downtown Treichville, the main retail district, an all-female march ended with a cacophony of gunfire lasting several minutes, witnesses said, without giving any details.
The U.N. and Western powers have warned Gbagbo he may face criminal investigation for crushing attempts at protest, although his military argues it has no choice because pro-Ouattara protesters are often armed and violent.
Dozens were killed during an attempted march on December 16, U.N. officials say, a protest that was followed by a wave of crackdowns on pro-Ouattara neighbourhoods in which scores were killed and many more kidnapped.
Additional reporting by Loucoumane Coulibaly; Writing by Tim Cocks; Editing by David Lewis and Matthew Jones