At least 76 people have died after torrential rainfall which has caused damages of around $2.5bn since March 19.
Iran’s Red Crescent has repeatedly complained that US banking sanctions reimposed last year make it impossible to receive donations from outside the country.
Washington “always claimed that it is on very good terms with the people of Iran [and] it is the Iranian government that it has a problem with,” Rouhani said on Wednesday before adding that by blocking aid to the Red Crescent, the US had given lie to that claim.
“The heads of the American regime have revealed their true vicious and inhuman nature,” he said at a cabinet meeting screened live on state TV.
State TV quoted Rouhani as saying that “if US officials were wise, they should have announced they would suspend the sanctions for one year because of the floods”.
The International Federation of Red Cross and Red Crescent Societies have estimated two million people need humanitarian aid following “the largest disaster to hit Iran in more than 15 years”.
The floods were a “historic test” for the American leadership, Rouhani said.
Last year, US President Donald Trump withdrew Washington from a multilateral agreement on Iran’s nuclear programme, later reimposing sanctions focussing on oil exports and financial transactions.
Iran’s Foreign Minister Mohammad Javad Zarif has accused the US of “economic terrorism”, saying its unilateral sanctions were impeding aid efforts to flood-stricken cities.
Iran has received material aid from neighbouring countries such as Pakistan and Kuwait as well as from Germany, France and Japan.
The head of the Iranian Red Crescent Society, Ali Asghar Peyvandi, criticised the US for blocking the Society for Worldwide Interbank Financial Telecommunication (SWIFT).
“We used a number of bank accounts connected to SWIFT, which we used for receiving international aid. But at the moment these accounts are subject to sanctions,” the Iranian Students News Agency quoted him as saying last month.
“It’s impossible to transfer cash from other countries as well as the International Federation of [Red Cross and] Red Crescent Societies,” he said.