By Katy Stech Ferek and Alex Leary

WASHINGTON -- Top Republican lawmakers led by Sen. Marco Rubio of Florida are calling on the Trump administration to reject a deal for TikTok if it leaves strong ties between the video-sharing app's Chinese owner and proposed partner Oracle Corp., citing national-security interests.

In a letter to President Trump on Wednesday, the Senate Republicans said they have significant concerns about a proposal to transfer the U.S. operations of TikTok and the agreement's data protections for the popular app's U.S. users. They asked for the president's assurance that Congress will be kept in the loop as a Treasury Department-led national-security review panel evaluates the deal this week.

The letter said that the current deal proposed by TikTok owner ByteDance Ltd. "appears to fall short of a full acquisition" by U.S.-based interests, leaving concerns about the Chinese government's potential access to U.S. user data going forward.

"Any deal between an American company and ByteDance must ensure that TikTok's U.S. operations, data, and algorithms are entirely outside the control of ByteDance or any Chinese-state directed actors, including any entity that can be compelled by Chinese law to turn over or access U.S. consumer data," said the letter, which was also signed by Sens. Thom Tillis (R., N.C.), Roger Wicker (R., Miss.), Rick Scott (R., Fla.), Dan Sullivan (R., Ark.) and John Cornyn (R., Texas).

The Oracle deal was reviewed Tuesday by the Committee on Foreign Investment in the U.S., which weighs business transactions with foreign entities for security concerns. The panel didn't immediately make a recommendation.

Asked about the status of the deal Wednesday, White House chief of staff Mark Meadows said the Trump administration would look to make sure national-security interests are protected.

"We're going to continue to review and make sure the interest of the American people," he said.

Another administration official said "there's a lot of analysis going on" over the particulars of the deal, with security of consumer data on the app and corporate control the key issues, and that top-level administration officials had not yet met on the issue as of Wednesday afternoon.

"Security is absolutely crucial," the official said. "That is the No. 1 thing, and probably the second is executive control, board control, ownership control."

In comments last month, Mr. Trump said he also expected the U.S. government to receive money as part of the deal. The official said that demand could be satisfied through the creation of a new TikTok-Oracle venture that would create "a lot of jobs and taxes."

The administration is also moving quickly, the official said, given a deadline Sunday in which TikTok could be banned if a deal isn't reached.

"The clock is ticking," the official said. "The president is very interested in this, so are a lot of other people."

In an August executive order, the White House effectively gave ByteDance a 45-day deadline to sell or restructure its U.S. TikTok operations or face a ban. The administration contends that the app poses a security threat because the data TikTok collects from U.S. consumers could be shared with the Chinese government. TikTok has said it would never hand over such data.

Other lawmakers have raised questions about national-security risks that arise from the Chinese government's access to Americans' personal data.

Earlier this week, Sen. Josh Hawley (R., Mo.) wrote Treasury Secretary Steven Mnuchin asking that he reject any Oracle-ByteDance collaboration. Treasury officials oversee the Committee on Foreign Investment in the U.S., a panel of national-security experts from Defense, State, Commerce and other departments that investigate business deals involving foreign money for risk.

"An ongoing 'partnership' that allows for anything other than the full emancipation of the TikTok software from potential Chinese Communist Party control is completely unacceptable," Mr. Hawley said in a letter on Monday.

Write to Katy Stech Ferek at katherine.stech@wsj.com and Alex Leary at alex.leary@wsj.com