The deputy commander of Iran's Revolutionary Guards said Washington had asked Tehran to respond "in proportion" after US forces killed top military commander Qassem Soleimani.
Soleimani, the commander of its Quds Force foreign operations arm, was killed before dawn Friday in a US drone strike in Baghdad, along with nine others, in an attack Tehran has vowed to avenge.
Hours later, the Americans "resorted to diplomatic measures... on Friday morning", the Guard's Rear-Admiral Ali Fadavi said on Iranian state television that night.
They "even said that if you want to get revenge, get revenge in proportion to what we did", he said, as quoted on the broadcaster's website.
Fadavi did not specify how Iran had received the message from its arch-enemy, even though Tehran and Washington have had no diplomatic relations for four decades.
Iran's Foreign Minister Mohammad Javad Zarif said in separate television interview on Friday night that "Switzerland's envoy transmitted a foolish message from the Americans this morning".
The Swiss official "was summoned in the evening and received a decisive response in writing... to the Americans' audacious letter," Zarif added.
The Swiss foreign ministry confirmed Saturday that its charge d'affaires had handed over a letter from Washington to the Iranians when he was summoned to the foreign ministry on Friday morning.
Switzerland's embassy in Tehran has represented US interests in the Islamic republic since ties were cut in 1980.
But Fadavi said the United States was not in a position "to determine" Iran's response.
"The Americans must await severe revenge. This revenge will not be limited to Iran," he said.
"The 'Resistance Front', with a vast geography, is ready to materialise this revenge," he added, referring to Iran's allies across the Middle East.
