By Danny Yadron and Devlin Barrett 

British Prime Minister David Cameron plans to lobby President Barack Obama this week to more publicly criticize U.S. technology companies, such as Facebook Inc., that offer encrypted communications that can't be unscrambled even with a court order, two people familiar with the matter said.

The move would extend Mr. Cameron's efforts to help intelligence and security officials access the information they say they need to help counter terrorism. One issue he and intelligence officials have highlighted in recent days is the growing use of encryption and the difficulty it poses for law enforcement. The U.S. Justice Department also has sought a way to access encrypted communications with a court order, but has been rebuffed amid civil-liberties concerns.

The move by Mr. Cameron, a Conservative, could put pressure on Mr. Obama to pick a side in a fight between privacy advocates and law enforcement over secret messaging in the digital age.

"Are we going to allow a means of communications which it simply isn't possible to read?" Mr. Cameron said in a speech Monday. "No. We must not."

Mr. Cameron also plans to mention his push to require social-media companies to proactively monitor their users to spot budding national-security threats, the people familiar with the matter said. Tech executives say that would be a nonstarter in the U.S.

Once a niche concern, encryption has been thrust into national debates after former National Security Agency contractor Edward Snowden leaked secrets on U.S. and British surveillance practices.

In response, U.S. tech companies, including Google Inc., Apple Inc. and Facebook, started taking extra steps to make sure spies couldn't read user data without court approval and their knowledge. This fall, Facebook's WhatsApp messaging service announced it had started a new type of encryption that even the company can't unscramble.

Apple drew rare public criticism from the Federal Bureau of Investigation last year when it announced the its new iPhone software would prevent police from viewing the information stored on a suspect's phone unless they learn his password--even if they have a search warrant.

FBI Director James Comey accused Apple of impeding law enforcement. But Apple hasn't backed down, and the White House warned Mr. Comey of picking a fight with one of the most popular companies in the U.S., American officials have said.

Apple and Facebook couldn't immediately be reached for comment Wednesday.

Mr. Cameron will try to push Mr. Obama "in the direction of what the FBI has said about this," a person familiar with the prime minister's intentions said.

A spokesman for Mr. Cameron declined to comment.

Though a spokeswoman, the White House declined to comment on a meeting that hasn't taken place yet.

Messrs. Cameron and Obama are scheduled to meet for a working dinner on Thursday, as well as additional meetings and a news conference on Friday.

The meeting comes amid increased concerns about radicalization and terror recruitment in the U.S. and Europe following the recent terrorist attacks in Paris. Al Qaeda in the Arabian Peninsula has claimed credit for that attack, though Western intelligence officials haven't substantiated those claims.

In addition to cybersecurity and technology issues, the leaders are expected to discuss the state of the economy, trade issues, and other foreign-policy topics including the war against Islamic State, counterterrorism efforts, Ebola and Russia.

Byron Tau contributed to this article.

Write to Danny Yadron at danny.yadron@wsj.com and Devlin Barrett at devlin.barrett@wsj.com

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