Speaking in a televised address, Khameini charged in a message directed at Washington: "No one trusts you. You are capable of bringing into our country a drug that will keep the virus alive and prevent its eradication."
Iran has been one of the countries worst hit by the Covid-19 illness along with Italy, Spain and China, and the latest fatalities raised the official death toll to 1,685, the health ministry said.
More than 1,028 new cases in the past 24 hours meant a total of 21,638 people had now tested positive for the virus, said ministry spokesman Kianouche Jahanpour.
US President Donald Trump -- who has imposed sanctions and a "maximum pressure" campaign on Tehran over its nuclear programme --- said on February 29 that Washington was ready to help Iran fight the virus if its leaders requested it.
But Khamenei reiterated Iran's rejection, charging that Washington, which whom it has had no diplomatic relations for more than 40 years, was "capable" of wanting to intensify the epidemic in the Islamic republic.
"Today America is our most ferocious and vicious enemy," Khamenei said in his address to the nation.
"The American leaders are liars, manipulators, impudent and greedy ... They are charlatans," he said, also labelling them "absolutely ruthless" and "terrorists".
The American proposals "to help us with medicines and treatments, provided we ask for them, are strange", he said, noting that the United States itself suffers from "a horrible shortage not only of disease prevention equipment but also of medicines".
Speaking to Washington, he added: "If you have something, use it for yourself."
Khamenei advised Iranians that "everyone should follow the instructions" of the authorities to fight the epidemic "so that Almighty God will put an end to this calamity for the Iranian people, for all Muslim nations and for all mankind".
The ministry's Jahanpour said Tehran province had reported 249 new cases and the central province of Yazd, where 84 new patients had been counted, "could become a new focus of the disease in the coming days".
To limit the spread of the virus, the authorities have asked people to refrain from travelling during the current Persian New Year celebrations.
In Iran "about 68% of deaths from Covid-19 disease are people over 60 years of age", Jahanpour said, stressing that family trips "are generally risk factors for this age group". - AFP