BEIRUT — Iran and the United States traded allegations of coronavirus mismanagement on Monday, accusing each other of endangering efforts to fight the pandemic as Iran intensified a campaign to pressure the United States into easing sanctions.

Iranian Foreign Minister Mohammed Javad Zarif said in a tweet that the United States is “impeding” the global fight to contain the spreading covid-19 disease by sustaining its sanctions, the latest salvo in a feud that escalated Sunday with comments by Iranian Supreme Leader Ali Khamenei suggesting America had created the coronavirus.

Secretary of State Mike Pompeo countered on Monday by saying that the “fabrications” by Khamenei about what Pompeo referred to as the “Wuhan Virus” put Iranians and people worldwide at risk.

In a statement, Pompeo listed ways he said the Iranian authorities had contributed to the spread of the virus: by lying about the true scale of Iran’s coronavirus crisis, by continuing flights to China as covid-19 was spreading, by stealing money intended for medical supplies and by hoarding medical equipment such as masks and gloves to sell on the black market.

Khamenei’s televised comments on Sunday were made in response to U.S. offers to send aid to Iran as Tehran struggles to contain the highest coronavirus infection rate in the Middle East. Khamenei said the United States could not be trusted to help because it “may” have created the coronavirus now sweeping the world.

“I do not know how real this accusation is, but when it exists, what wise man would trust you to bring them medication?” Khamenei said, addressing the United States. “Possibly your medicine is a way to spread the virus more.”

He added: “You might send people as doctors and therapists, and maybe they would want to come here and see the effect of the poison they have produced in person.”

The Iranian leader also pointed out that the United States is failing to curtail the spread of the disease at home. If America has help to offer, “spend it on yourselves,” he said.

“You have shortages yourself,” he said. “Statements by American officials . . . are explicitly saying they have major shortages, both in terms of preventive equipment and also medicine.”

The spat over responsibility for the coronavirus’s spread came as Iran and America both battle escalating rates of infection among their populations. Over the weekend, the United States overtook Iran and other nations to become the country with the third-largest number of confirmed coronavirus cases in the world, with more than 40,000 reported as of Monday. Iran said Monday that the number of infections in the previous 24 hours had climbed by 1,411 to 23,049, with 127 deaths, bringing the toll to 1,812.

There have been indications, however, that Iran has failed to disclose the true number of people afflicted, including satellite and video evidence that Iran was digging vast graves for victims just days after announcing the first cases.

Iran has blamed the crippling U.S. sanctions imposed by the Trump administration for the difficulties the country has confronted, saying they have contributed to shortages of preventive equipment such as face masks and gloves as well as medicine.

In a speech to the Iranian cabinet carried live on Iranian television Monday, President Hassan Rouhani called America’s offers of help “the biggest lie.”

“If they want to help Iran, all they need to do is to lift sanctions . . . Then we can deal with the coronavirus outbreak,” he said.

In his tweet, Zarif urged countries around the world to ignore the U.S. sanctions, which target most sectors of the Iranian economy. “The ONLY remedy: DEFY U.S. mass punishment,” he wrote.

Pompeo said in his statement that there is no evidence U.S. sanctions have interfered with Iranian efforts to procure medicine or equipment for the coronavirus effort. “U.S. sanctions do not target imports of food, medicine and medical equipment, or other humanitarian goods,” he said.