By Alison Sider and Ted Mann

The Trump administration threatened Wednesday to bar mainland Chinese airlines from flying to and from the U.S. starting later this month, saying Beijing has failed to approve resumption of these routes by U.S. carriers.

The threat of a ban was the latest sign of souring U.S.-China relations that are at their worst in more than three decades.

Some U.S. airlines have sought to resume service to China this month after suspending flying there earlier this year, as the coronavirus pandemic took hold.

The U.S. Transportation Department, led by Secretary Elaine Chao, said Wednesday that the Civil Aviation Administration of China hasn't approved requests by United Airlines Holdings Inc. and Delta Air Lines Inc. to resume flights. The DOT accused China of violating an agreement that governs air travel between the two countries.

The transportation agency said it would reconsider its planned ban, if Chinese regulators adjust their policies to allow U.S. carriers to return. "Our overriding goal is not the perpetuation of this situation, but rather an improved environment wherein the carriers of both parties will be able to exercise fully their bilateral rights," the DOT's order said. "Should the CAAC adjust its policies to bring about the necessary improved situation for U.S. carriers, the Department is fully prepared to revisit the action it has announced in this order."

Chinese carriers continued to fly passengers between the U.S. and China even after U.S. carriers had stopped flying in February and March, albeit at reduced levels. Currently four Chinese airlines -- Air China Ltd., China Southern Airlines Co., Xiamen Airlines and China Eastern Airlines Corp. -- operate scheduled passenger flights between the two countries, the Transportation Department said. Other Chinese carriers that were planning to add flights in the coming months, according to filings with the Transportation Department, would be barred from doing so under the order.

The order blocking Chinese carriers is set to go into effect June 16 unless revoked. President Trump could opt to put it into effect sooner. A White House spokesman declined to comment on whether the president would do so. The order affects only mainland Chinese carriers, not Hong Kong carriers, a spokesman for the Transportation Department said.

The Chinese Embassy in Washington didn't immediately respond to a request for comment.

Airline access joins a lengthening list of sore spots in U.S.-China relations that continue to spiral toward open across-the-board rivalry. While both sides struck a trade deal that promises to boost Chinese purchases of U.S. farm products, many other business issues -- including market access, investment and technology -- have become points of contention.

The airline issue strikes at a central tenet of the Trump administration's China policy -- the need for reciprocity in relations that the administration says have been tilted in Beijing's favor. As a result, both governments have expelled reporters from the other's country, and the Trump administration last week said it is scrutinizing Chinese firms listed on U.S. stock markets.

A senior administration official said Wednesday that while the move on airlines wouldn't have much practical impact on travel, with most flights flying at minimal capacity, the threat demonstrated the Trump administration's focus on reciprocity in its dealings with China. "If they keep escalating, we're going to keep escalating," this official said.

At the outset of the year, U.S. and Chinese airlines operated 325 weekly flights between the two countries. In late January as the new coronavirus had started to spread, the Trump administration imposed travel restrictions on foreign nationals who have been in China, but it didn't halt flying between the two countries. By mid-February, there were about 20 weekly flights, all operated by Chinese carriers.

Meanwhile, China set limits on international service for Chinese carriers and for foreign airlines flying to the country in March.

The DOT has argued that the limits effectively keep U.S. airlines out, since they are based on scheduled flying levels in mid-March -- after U.S. airlines had already suspended their flights to China because of growing virus fears.

Now, U.S. carriers are slowly beginning to expand their international flying. Delta had applied to start flying to China again June 1, but its plans have been delayed by the regulatory limbo. Now, the carrier said, it hopes to fly to Shanghai via Seoul from Detroit and Seattle in the second half of June, subject to government approval. United has said it would restart three China routes June 15, if regulators approve.

Delta on Wednesday said it supported the U.S. government's actions, and United said it looked forward to resuming flights when the regulatory issues are resolved.

Airlines for America, a trade association, said the DOT's order will protect the rights of U.S. carriers and "ensure fair and equal opportunity for passenger airlines with respect to service to and from China."

The dispute over resuming flights has been ramping up for weeks. The U.S. government has repeatedly raised its objections with Chinese authorities, including in a May 14 call, according to the DOT order. In a letter to the DOT last week, Chinese aviation officials said they didn't believe they were violating the agreement between the two countries and didn't say when they would revise their order regarding U.S. airlines' flights.

In the order on Wednesday, the agency said it would impose further limits on charter flights by Chinese carriers to repatriate Chinese citizens stuck abroad. The agency said it had "learned through diplomatic channels" that Chinese airlines could be using such flights to circumvent limits on scheduled service.

The U.S. and China have been engaged in tit-for-tat conflicts over everything from trade policy to conspiracy theories over the origins of the new coronavirus.

Momentum toward a larger trade deal has been slowed by the coronavirus, which emerged in the Chinese city of Wuhan before exploding into a global pandemic. The pandemic is a new topic of dispute between the nations.

Mr. Trump has blamed China for a slow public response to the virus, and his administration has publicly said it was investigating theories that the virus escaped from a Chinese lab in the city.

A spokesman for the Chinese foreign ministry tweeted that the virus had actually been brought to China by the U.S. military, a post flagged by the social media service as suspect.

Neither of the dueling origin stories for the virus has been substantiated.

In recent days, Chinese state media has played up images of the domestic unrest in U.S. cities, including Mr. Trump's decision to forcibly clear peaceful demonstrators against police violence from a public park outside the White House.

Write to Alison Sider at alison.sider@wsj.com and Ted Mann at ted.mann@wsj.com