One of the exceptions is the political party that organized Sunday's rally in Karachi, the Muttahida Quami Movement. The party's chief, Altaf Hussain, criticized both Islamic and other mainstream political parties for failing to organize rallies to protest the attack on Malala.
He called the Taliban gunmen who shot the girl "beasts" and said it was an attack on "the ideology of Pakistan."
"Malala Yousufzai is a beacon of knowledge. She is the daughter of the nation," Hussain told the audience by telephone from London, where he is in self-imposed exile because of legal cases pending against him in Pakistan. His party is strongest in Karachi.
Many of the demonstrators carried the young girl's picture and banners praising her bravery and expressing solidarity.
Malala earned the enmity of the Pakistani Taliban for publicizing their behavior when they took over the northwestern Swat Valley, where she lived, and for speaking about the importance of education for girls.
The group first started to exert its influence in Swat in 2007 and quickly extended its reach to much of the valley by the next year. They set about imposing their will on residents by forcing men to grow beards, preventing women from going to the market and blowing up many schools — the majority for girls.
Malala wrote about these practices in a journal for the BBC under a pseudonym when she was just 11. After the Taliban were pushed out of the Swat Valley in 2009 by the Pakistani military, she became even more outspoken in advocating for girls' education. She appeared frequently in the media and was given one of the country's highest honors for civilians for her bravery.
Many hope the shooting of Malala will help push the military to undertake a long-awaited offensive in the Pakistani Taliban's last main sanctuary in the country in the North Waziristan tribal area.
The Pakistani Taliban said they carried out the shooting because Malala was promoting "Western thinking." Police have arrested at least three suspects in connection with the attack, but the two gunmen who carried out the shooting remain at large.
Associated Press writers Zarar Khan and Munir Ahmed in Islamabad contributed to this report.