"We hold America responsible for Iranians' safety amid the new coronavirus outbreak", Khabaronline quoted Rabiei as saying.
Mr. Rabiei said it seems as if the U.S.is more willing to "bring the situation to an end" than it has been in the past, according to the AP.
In a rare act of cooperation, the two countries swapped prisoners in late 2019 - U.S. graduate student Xiyue Wang, detained for three years on spying charges, and imprisoned Iranian stem-cell researcher Massoud Soleimani, accused of violating sanctions.
Relations have grown more hostile again since 2018 when Trump exited Iran's 2015 nuclear deal with major powers and re-imposed sanctions on Tehran that has crippled its economy.
United States officials last week said they were making progress in efforts to secure the release of a detained Navy veteran in Iran.
The New York Times previously reported that Tehran and Washington were holding negotiations on exchanging a US Navy veteran, Michael R. White, for an unidentified doctor held by the US.
US officials are denying reports of a coronavirus-initiated prisoner swap with Iran that could mean the return of a Navy veteran to the United States and a 60-year-old university professor to Tehran.
"We have stated our readiness to discuss the release of all prisoners without preconditions ... but Americans have not responded yet".
U.S. Secretary of State Mike Pompeo called on Iran in March to release on humanitarian grounds all wrongfully detained Americans held in the country.
In March, the family of former Federal Bureau of Investigation agent Robert Levinson, who vanished in Iran 13 years ago, said they had been informed by US officials that they had determined that Levinson was probably dead.
One of them is Sirous Asgari, an Iranian scientist infected with the novel coronavirus while in detention, according to the Iranian foreign ministry. Switzerland looks after USA interests with Tehran.
U.S. officials said on Tuesday that they were set to deport Asgari, who was acquitted of stealing trade secrets.
While the exchange represented a rare win for both countries, it came as Iran faced crushing United States sanctions and followed nationwide protests that reportedly saw more than 200 people killed.
It is not clear exactly how many Americans Iran may hold, but they include father and son Baquer and Siamak Namazi and environmental expert Morad Tahbaz.
Hostility between the countries reached historic heights this year. Iran retaliated on January 9 by firing missiles at bases in Iraq where United States troops were stationed.