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 June 16, saying Beijing has failed to approve resumption of these routes by U.S. carriers.

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 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. It accused China of violating an agreement that governs air travel between the two countries.

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.

The order blocking Chinese carriers is set to go into effect June 16, but 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 doesn't affect Hong Kong, only mainland Chinese carriers, a spokesman for the DOT said.

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

Both sides struck a trade deal that promises to boost Chinese purchases of U.S. farm products. Administration officials said in February that China was abiding by the terms of the first phase of a trade deal that took effect that month, including a $32 billion increase in Chinese purchases of American grain over two years. China meanwhile announced it would begin excluding some American goods from tariffs that had been slapped on during the escalating trade war that marked the first 2 1/2 years of Mr. Trump's presidency.

But 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 showed how the Trump administration was focused 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. By mid-February, there were just 20, all operated by Chinese carriers. The Chinese carriers have since added some flights.

China set limits on international service for Chinese carriers and for foreign airlines flying to the country in March, to help stem the spread of coronavirus.

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.

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 novel 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