British government officials will meet with representatives of American technology companies this week to demand that they do more to help in the fight against terrorism and online hate speech, the latest move in a widening global push against encryption technology that blocks access to the private messages of criminal and innocent users alike.

The meeting on Thursday comes after Amber Rudd, Britain’s home secretary, said that the country’s intelligence agencies should have access to encrypted messages sent through WhatsApp, the internet-messaging service owned by Facebook. Her remarks were part of the British response to the fatal terrorist attack last week in London, when Khalid Masood, a 52-year-old Briton, drove a car into pedestrians before attacking a police officer.

Tech companies and digital rights advocates have said that such efforts would infringe on human rights because providing the authorities with access to such messaging services would require weakening their overall levels of encryption. That, they argue, would leave people who use those services vulnerable.

But after several terrorist attacks in Europe, the region’s lawmakers and some of their counterparts in the United States now want Silicon Valley companies to do more to tackle potential threats.

For many policy makers, that includes opening up services like WhatsApp and Telegram, a rival internet messaging tool, to national intelligence agencies when they are investigating terrorist activities.

“We do want them to recognize that they have a responsibility to engage with government, to engage with law enforcement agencies when there is a terrorist situation,” Ms. Rudd told the BBC on Sunday, referring to tech companies. “They cannot get away with saying we are in a different situation. They are not.”

Ms. Rudd’s demands are expected to be repeated in person at the session with the tech executives, although no further details of the meeting have been released.

Lena Pietsch, a Facebook spokeswoman, said in an email: “We are horrified by the attack carried out in London” and “are cooperating with law enforcement” as the investigation continues.

The move by British lawmakers is the latest effort in Europe to police how internet giants operate online. This month, a German government minister said that he would propose new legislation that could fine tech companies around $50 million if they failed to stop hate speech being spread on digital platforms like Facebook, Twitter and Google’s YouTube.

A number of high-profile brands and advertisers have recently pulled their marketing from these online services after their ads were displayed next to potential hate speech.

Officials in Britain, however, are going a step further. And by demanding that intelligence agencies be allowed to read encrypted messages, Ms. Rudd is reiterating yearslong plans to gain more control over digital services.

Last year, the country passed legislation giving law enforcement greater powers to make telecommunications and technology companies hand over digital information relating to intelligence operations. The law also required tech companies to bypass encryption protocols, where possible, to aid ongoing investigations.

In the United States, the authorities have made similar demands. The F.B.I. asked Apple to unlock the iPhone used by one of the attackers who killed 14 people in San Bernardino, Calif., in December 2015. Apple resisted, and the F.B.I. later said it had found a way to unlock the phone without the company’s help.

Tech companies say they cannot hand over such information because internet messages are sent through so-called end-to-end encryption.

This technology scrambles messages to make them indecipherable to anyone but their intended recipient. It also makes messages unreadable when they pass through an app’s server, meaning companies do not have the ability to provide the information to law enforcement even if they wanted to.

If such technology is weakened, campaigners say, governments and hackers could gain access to encrypted messages, weakening people’s ability to communicate online.

“Compelling companies to put back doors into encrypted services would make millions of ordinary people less secure online,” said Jim Killock, executive director of Open Rights Group, a British nonprofit. “We all rely on encryption to protect our ability to communicate, shop and bank safely.”