These behind-the-scenes conversations signal how tensions over TikTok have simmered in Washington. While the app appeared to fade as a political flashpoint after Mr. Trump left office last year, lawmakers and government officials have privately grown frustrated over the Biden administration’s lack of progress in policing TikTok and other Chinese apps that could leak data to Beijing.

That dissatisfaction has boiled over into public view in recent months, after new revelations from BuzzFeed and other news outlets about TikTok’s data practices and ties to its Chinese parent. Mr. Rubio and Mr. Warner have recently called for a Federal Trade Commission investigation into the app, while a regulator at the Federal Communications Commission publicly said that TikTok should be booted from American app stores.

A group of Republican senators has also demanded answers from TikTok about who could access the app’s data. On Tuesday, officials in the House of Representatives told staff members that they did not recommend using or downloading the service, citing security concerns, according to an email obtained by The New York Times.