Messaging platform Signal said on Friday it was experiencing "technical difficulties" as it worked to accommodate millions of new users.
Some users reported messages failing to send on both the mobile and desktop apps for several hours.
The company has seen a huge uptick in interest since its rival WhatsApp unveiled new privacy terms last week.
On Twitter, Signal said it had added servers "at a record pace" and was working to restore service.
"Millions upon millions of new users are sending a message that privacy matters," it said in a tweet.
Both Signal and Telegram, another free-to-use encrypted messaging app, have benefited from discontent sparked by WhatsApp's updated terms and conditions.
WhatsApp told its two billion users they must allow it to share data with its parent company Facebook if they wished to continue using it.
This does not apply to users in the UK and Europe - but the notification was sent to everyone.
WhatsApp stressed that its practice of sharing data with Facebook was not new, and was not being expanded. It said there had been "confusion" about its message, which initially gave people until 8 February to accept its updated terms or stop using the service.
WhatsApp has now changed the cut-off date to 15 May, saying it would use the time to clear up misinformation.
"We can't see your private messages or hear your calls, and neither can Facebook," WhatsApp said in an earlier FAQ blog post.
According to data from analytics firm Sensor Tower, Signal was downloaded 246,000 times worldwide in the week before WhatsApp announced the change on 4 January, and 8.8 million times the week after.
In India, downloads went from 12,000 to 2.7 million. In the UK, they leapt from 7,400 to 191,000, and in the US from 63,000 to 1.1 million.
On Wednesday, Telegram said it had surpassed 500 million active users globally. Downloads jumped from 6.5 million in the week starting 28 December, to 11 million during the following week.
During the same period, WhatsApp's global downloads shrank from 11.3 million to 9.2 million.
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