That remains to be seen, but the protests have already gained enough attention to provoke angry reactions in some quarters.

“These protests are done by instigators, saboteurs and vandalists and anarchists,” said one critic, Kazem Anbarlooie, the editor in chief of the hard-line newspaper Resalat. “Recently our enemies were communists and liberals, now Americans are provoking masochists against us.”

The first protest in December took place on a Wednesday and seemed connected to the White Wednesday campaign, an initiative by Masih Alinejad, an exiled Iranian journalist and activist living in the United States. Ms. Alinejad has reached out to Iranian women on Persian-language satellite television and through social media, and via a website she runs called My Stealthy Freedom. On the website, women post images of themselves without head scarves, demanding an end to the compulsory head scarf law.

During Monday’s protests some women waved white scarves, the symbol of Mrs. Alinejad’s campaign.

Hard-liners say that foreign intelligence agencies, including the Central Intelligence Agency, have been nurturing protests in Iran, like those that broke out in 80 cities at the end of last year. Nearly 4,000 people were arrested and 25 died, according to official statistics. The hard-liners have not provided proof to back up their claims.

The Islamic head scarf, or hijab, is seen by Iranian ideologues as a pillar of the Islamic Republic of Iran. The law regarding the scarf has been enforced since the 1979 Islamic Revolution, and a head scarf is obligatory for every woman in the country, even tourists and visiting foreign dignitaries.

While discriminatory Islamic divorce and inheritance laws pose problems for individual women, the head scarf is a highly public symbol of a set of personal rules imposed by Iran’s clerical leaders, who decide what people can wear, what music they can listen to and what television programs and movies they get to see. Men are also the subject of clothing laws: They are forbidden to wear shorts in public.

During the past decade, influenced by the rise of the internet, satellite television and cheap foreign travel, many Iranians have grown deeply resentful of rules that they can see for themselves are out of step with most of the rest of the world. Many have become relatively secular and feel increasingly unwelcome in the fixed-in-stone state version of Shiite Islam, and many have taken to flouting the rules whenever and wherever they feel free enough to do so.