ISLAMABAD, Pakistan — Violent crowds furious over an anti-Islamic video made in the United States convulsed Pakistan’s largest cities on Friday, leaving up to 19 people dead and more than 160 injured in a day of government-sanctioned protests.

It was the worst single day of violence in a Muslim country over the video, “Innocence of Muslims,” since protests began nearly two weeks ago in Egypt, before spreading to two dozen countries. Protesters have ignored the United States government’s denunciation of the video.

Peaceful protests had been approved by Pakistan’s government, which declared Friday a national holiday, the Day of Love for the Prophet Muhammad. The move was part of an effort to either control or politically capitalize on rage against the inflammatory video, which depicts Muhammad, the founder of Islam, as a sexually perverted buffoon.

Friday’s violence began with the fatal shooting of a television station employee during a protest in the northwestern city of Peshawar, and was amplified through armed protests in the southern port city of Karachi that left 12 to 14 people dead, Pakistani news media reported.