TUNIS — Tunisia has long been regarded as a pioneer for women’s rights in the Arab world, but the day-to-day life of many Tunisian women is still one of abuse and harassment. So when Parliament passed a measure last week outlawing violence against women, some burst into ululation and passed around bouquets of jasmine.

The new law makes it easier to prosecute domestic abuse, and it imposes penalties for sexual harassment in public spaces. It says that citizens are entitled to notify the police if they witness violence against women, and that children should be educated in schools about human rights. And it calls for both the police and judges to be trained on how to handle violence against women.

Tunisia already stood out among Islamic countries because of its legal arsenal of protections for women. Its code of personal status, adopted in 1956, allows divorce and outlaws polygamy, for example. But women’s rights associations and human rights groups say the new law is a major step forward, in part because it so broad, outlawing not just physical violence but psychological abuse and even economic discrimination.

“This is why the new law is so important, because it also takes care of the preventive side of violence against women in general, not only the reform of the criminal side,” Monia Ben Jemia, president of the Tunisian Association of Democratic Women, said in an interview.