JERUSALEM — Women working in Palestinian Arab television in Gaza have been ordered to avoid walking alone in the street after radical Islamists threatened to slit their throats if they do not dress in religious garb while on air.

The threat from the extremist fringe group Swords of Truth is being taken seriously by female journalists and television presenters, who staged a march in protest at the action yesterday.

Vigilantes from the group have bombed Internet cafés, shops, pool halls, a restaurant, and a Christian bookstore in recent weeks.

“We will cut throats, and from vein to vein, if needed to protect the spirit and morals of this nation,” read a statement sent to news organizations in Gaza on Friday. The group accused the women of being “without any shame or morals.”

“Yesterday, I was just sitting down and thinking, if I died, who is going to take care of my two kids?” said Lana Shaheen, 35, the Syrian-born head of English programming at Palestine TV in Gaza and an on-air correspondent for a Jordanian television network.

Ms. Shaheen, who has lived in Gaza for 11 years with her Palestinian Arab husband, does not wear a headscarf. And while many of her colleagues do cover their heads, they also “wear jeans, like all journalists everywhere.”

Yesterday, Radwan Abu Ayyash, the Palestinian Arab deputy minister of culture, condemned the threat as coming from criminals who did not understand Islam. But he said extra precautions would have to be taken nonetheless.

“The women themselves will have to be protected. … The families and the police might work together” in arranging escort cars and more bodyguards, Mr. Abu Ayyash said.