The ban would apply to Skype as well as the WhatsApp, Viber and Tango smartphone- and computer-based applications. Facebook messenger and Twitter appear to be exempt.
The measure would need to be approved by the Pakistan Telecommunication Authority. A spokesman for the PTA said it would refer the request to Prime Minister Nawaz Sharif’s government.
In a statement, Pakistan’s interior minister, Chaudhry Nisar Ali Khan, appeared skeptical of the request.
“So far no decision has been made to ban Skype, Viber, WhatsApp and other networks,” he said. “Personally, I am not in favor of this ban because I think it is of no use. . . . We will look into it.”
In recent years, Karachi has reported about 2,000 killings and another 2,000 kidnappings annually as rival gangs and militant groups, including Taliban leaders from Afghanistan, seek to mark turf in the rapidly growing city of at least 15 million people.
Increasingly embarrassed by perceptions that the country’s economic hub is lawless, Pakistani officials began targeted operations in Karachi last month.
Though smartphones are less common in Pakistan than in Europe or the United States, Skype is used by a range of consumers to make international calls without incurring high usage charges.
A ban in Karachi, even temporary, could further cement Pakistan's image as one of the most restrictive nations in the world for Internet use.
The telecommunications authority already bans more than 4,000 Web sites for what it considers objectionable material, including YouTube, which was blocked last year after a California man posted a video that much of the Muslim world deemed blasphemous.
In a report issued Thursday, the pro-democracy group Freedom House named Pakistan as one of 14 countries in the world where the Internet is “not free.”
The Washington-based group said Pakistan blocks objectionable content, monitors Internet users, lacks adequate connectivity in rural areas and has not done enough to protect users from accusations of blasphemy.
In addition to Pakistan, the group also gave a “not free” rating to Burma, Sudan, United Arab Emirates, Belarus, Saudi Arabia, Bahrain, Vietnam, Uzbekistan, Ethiopia, Syria, China, Cuba and Iran.
Shaiq Hussain contributed to this report.