ABC News first reported the details of the Russian cargo plane, including Russia's invoice and concerns expressed privately by U.S. officials at the time that the 45 ventilators included onboard might have "voltage-related" issues.
The Russian ventilators have not been used in U.S. hospitals and remain in storage.
"These misguided decisions waste millions of U.S. taxpayer dollars, undermine our foreign policy and national security interests, and impair our nation's ability to combat the coronavirus crisis," wrote the Democratic chairs, including Rep. Carolyn Maloney, D-N.Y., who oversees the House Oversight and Reform Committee, and Eliot Engel, D-N.Y., who oversees the House Foreign Affairs Committee.
Signing the letter were the top Democrats overseeing State Department funding and House-led investigations into the coronavirus crisis. In addition to Maloney and Engel, the letter also was signed by Nita Lowey of New York, chairwoman of the House Appropriations Committee; Rep. James Clyburn of South Carolina, chairman of a select subcommittee on coronavirus; and Stephen Lynch of Massachusetts, national security subcommittee chair on House Oversight and Reform.
The Trump administration has not said whether the U.S. might get a discount on Russia's aid bill now that the U.S. has agreed to send 200 ventilators its way.
In a statement provided Friday to ABC, the Federal Emergency Management Agency (FEMA) referred questions on the status of Russia's $659,283 invoice to the State Department, which did not provide comment.
"The flight contained 45 ventilators, over 90,000 gloves of various types, and other medical supplies such as medical clothing and respirators. This was a mix of donated goods and goods purchased by the US State Department," FEMA wrote.
One source familiar with the shipments said the cargo flights were not a swap and that the two shipments were considered unrelated. The person spoke on condition of anonymity because they were not authorized to speak publicly.
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Earlier this spring, as the spike of coronavirus cases prompted fears of a ventilator shortage in New York and New Jersey, Putin offered to send the U.S. the aid shipment.
The April 1 cargo flight that landed at New York City's John F. Kennedy airport included thousands of pieces of equipment not typically used by hospitals, including chemical warfare-style gas masks and household cleaning gloves, as well as 45 ventilators and thousands of surgical gloves, medical clothing and antiseptic packets.
"It was a very nice gesture on behalf of President Putin and I could have said 'no thank you' or I could have said 'thank you' and it was a large plane of very high-quality medical supplies, and I said 'I'll take it,'" Trump told reporters April 2.
New York and New Jersey wound up returning the Russian ventilators to the federal stockpile after reports that several coronavirus patients in St. Petersburg were killed in fires linked to overloaded ventilators.
"Out of an abundance of caution, the states are returning the ventilators to FEMA," a spokesperson said in a statement released earlier this month. "The conclusion(s) of the investigation being conducted by the Russian authorities into the fire in St. Petersburg will help inform our decision regarding any future use of the ventilators."
Since then, the State Department has agreed to send 200 ventilators to Russia, which has the third largest number of cases of COVID-19 in the world. The first batch of 50 ventilators were delivered on May 21, with another 150 ventilators expected to ship next week, according to a senior administration official.
The ventilators are being manufactured by Vyaire Medical in California and will be donated to the Pirogov National Medical and Surgical Center in Moscow.
Russia isn't alone. The U.S. has agreed to provide more than 15,000 ventilators to more than 60 countries, including in Europe.
Democrats are also questioning why the U.S. would buy ventilators manufactured by a subsidiary of a company currently under U.S. sanctions as a result of Moscow's 2014 aggression against Ukraine.
According to Russia's foreign ministry, the money for the supplies came from the Russian Direct Investment Fund -- Russia's sovereign wealth fund that was sanctioned by Treasury in June 2015 as part of sanctions punishing Russia for its annexation of Crimea from Ukraine.
Also, at least some of the ventilators were made by a Siberian factory that is owned by a Russian state company sanctioned by the U.S. over Russia's invasion of Ukraine in 2014.
Sanctions on the Russian Direct Investment Fund don't apply to medical equipment and supplies.
ABC News' Ben Gittleson contributed to this report.