For Facebook, the move also offers avenues for making money from Instagram and WhatsApp. WhatsApp currently generates little revenue; Instagram produces ad revenue but none from its messaging. Mr. Zuckerberg does not yet have specific plans for how to profit from integrating the services, said two of the people involved in the matter. A more engaged audience could result in new forms of advertising or other services for which Facebook could charge a fee, they said.

One potential business opportunity involves Facebook Marketplace, a free Craigslist-like product where people can buy and sell goods. The service is popular in Southeast Asia and other markets outside the United States.

When the apps are knitted together, Facebook Marketplace buyers and sellers in Southeast Asia will be able to communicate with one another using WhatsApp, which is popular in the region, rather than using Facebook Messenger or another, non-Facebook text message service. That could eventually yield new ad opportunities or profit-generating services, said one of the people.

Some Facebook employees said they were confused about what made combining the messaging services so compelling to Mr. Zuckerberg. Some said it was jarring because of his past promises about independence. When Facebook acquired WhatsApp for $19 billion in 2014, Mr. Koum talked publicly about user privacy, and said, “If partnering with Facebook meant that we had to change our values, we wouldn’t have done it.”

Last month, during one of WhatsApp’s monthly meetings for staff members, it became clear that Mr. Zuckerberg’s mandate would be a priority in 2019, said a person who was there. One WhatsApp employee then conducted an analysis of how many potential new users in the United States the integration plan could bring to Facebook, said two people familiar with the study. The total was relatively meager, the analysis showed.

To assuage concerns, Mr. Zuckerberg called a follow-up meeting with WhatsApp employees a few days later, three of the people said. On Dec. 7, employees gathered around microphones at the WhatsApp offices to ask him why he was so invested in merging the services. Some said his answers were vague and meandering. Several WhatsApp employees have left or plan to leave because of Mr. Zuckerberg’s plans, the people said.

Unifying the infrastructure for WhatsApp, Instagram and Facebook Messenger is technically challenging. Unlike Facebook Messenger and Instagram, WhatsApp does not store messages and keeps minimal user data. It is the only one of the services to currently use end-to-end encryption by default.