The Biden administration is considering pushing Congress to give it more legal power to deal with TikTok and other technology that could expose sensitive data to China, five people with knowledge of the matter said, as it comes under growing pressure to resolve security concerns about the Chinese-owned video app.

White House officials are weighing whether to support legislation being developed by Senator Mark Warner, Democrat of Virginia, that would give the government more authority to police apps and services that could pose a risk to Americans’ data security or be used in foreign influence campaigns, two of the people said. That could be used to target TikTok, which is owned by the Chinese company ByteDance.

The administration has provided feedback on the draft bill, which would offer an alternative to legislation that outright bans the app, the two people said. Mr. Warner said Sunday on Fox News that he planned to introduce the bill this week alongside Senator John Thune, Republican of South Dakota. It’s unclear exactly how the administration would back Mr. Warner’s bill or other legislation should it choose to do so.

The growing focus on Congress is a significant shift in the White House’s strategy to respond to concerns about TikTok. Since President Biden took office, his administration has privately negotiated a deal that would allow TikTok to operate in the United States while mitigating national security concerns about it. Under Chinese law, critics have said, the app could be compelled to turn over personal data it has collected about millions of Americans to Chinese authorities. And they fear Beijing could use TikTok to deliver political messages to people’s smartphone screens.