It was a heated exchange on Monday, when Facebook executives and Attorney General William Barr argued over whether encryption messaging products should be open to law enforcement, or is it a violation of privacy. The situation looks to be escalating a standoff over privacy and policing.

The executives overseeing Facebook’s WhatsApp and Messenger, Will Cathcart and Stan Chudnovsky, sent a letter to the attorney general saying that creating a so-called encryption backdoor into their services for law enforcement would affect the privacy and safety of users.

“The ‘backdoor’ access you are demanding for law enforcement would be a gift to criminals, hackers and repressive regimes, creating a way for them to enter our systems and leaving every person on our platforms more vulnerable to real-life harm,” the executives said. Their letter was sent ahead of a Senate hearing on Tuesday about encryption, at which Facebook and Apple executives testified.

At an afternoon event, Mr. Barr said dealing with problems that strong encryption created for law enforcement was one of the Justice Department’s “highest priorities.”

The attorney general believes criminals are increasingly using and hiding behind messaging apps that are not accessible to investigators’ even with a warrant. Companies like Facebook are selling the idea that “no matter what you do, you’re completely impervious to government surveillance,” Mr. Barr said.

“Do we want to live in a society like that?” he asked. “I don’t think we do.”

The fight between tech companies and law enforcement officials over how to balance privacy and security with digital communications has been going on for a while. Not only Facebook but also Apple is involved, and it promises to become more intense as more messaging services become encrypted.