By Michael C. Bender and Andrew Restuccia

WASHINGTON -- President Trump has told advisers he is uncomfortable with a pending deal for Oracle Corp. to become TikTok's U.S. technology partner, according to people familiar with conversations, in another sign that the proposed tie-up isn't yet a done deal.

Mr. Trump's private concerns were echoed publicly on Thursday by White House chief of staff Mark Meadows, who cautioned that a deal that leaves the company predominantly Chinese-controlled might not meet the president's standards.

"My big concern is if all we're doing is repackaging it and still keeping it as a predominantly Chinese government-run company, that would not set well with the original goals the president outlined," Mr. Meadows told reporters at the White House.

Mr. Meadows said the administration is still reviewing the details of the agreement.

Mr. Trump on Wednesday expressed discomfort with any agreement that leaves ByteDance Ltd., the Beijing-based company that owns TikTok, with majority ownership of the company's U.S. operations. "Conceptually, I can tell you, I don't like that," he told reporters.

ByteDance's push to retain majority ownership is causing widespread concerns within the administration and among some Senate Republicans.

The Wall Street Journal reported Wednesday that Trump administration officials were working toward a structure that would give American investors a majority share of the company that will take over the Chinese-owned video-sharing app TikTok.

In a conference call on Wednesday night, ByteDance officials agreed to significant strengthening of the data security and data management aspects of the proposal, according to a person familiar with the matter. Treasury Secretary Steven Mnuchin participated in the call, this person said.

The 20-page agreement, highly technical in nature, amounted to a Treasury counterproposal on the security issues, the person said. Those had emerged as the most significant concerns in the TikTok negotiations for some China hawks, even overshadowing the issue of corporate ownership and control.

In a further complication, Chinese authorities will have to approve the terms of the deal, Bytedance noted on Thursday -- so any deal struck by Oracle and ByteDance will face scrutiny from Beijing as well as the White House.

--John D. McKinnon contributed to this article.

Write to Michael C. Bender at Mike.Bender@wsj.com and Andrew Restuccia at Andrew.Restuccia@wsj.com