"What is certain in this regard is that the hands of time will not turn backwards, and the nations and lands of the region will no longer serve as shields for American bases," said Khamenei, in a Hajj message.
He said the United States, "in addition to no longer having any safe haven in the region for aggression and the establishment of military bases, is moving further and further away from its former position with each passing day".
The remarks come as Iran and the United States continue exchanges aimed at reaching a deal to end the war, which began on February 28 and spread across the region.
A fragile ceasefire has been in place since April 8.
Iran's foreign ministry has said Tehran and Washington reached understandings on many issues in exchanges over a deal for ending the war, but warned an agreement was not yet imminent.
On Tuesday, Iran's Revolutionary Guards said they had downed a US drone and shot at other aircraft attempting to enter the country's airspace, without specifying when the incidents took place.
In a statement, the Guards further warned "against any violation of the ceasefire by the aggressor US military and considers its right to reciprocal response legitimate and certain."
On Monday, the US Central Command said forces attacked missile sites in southern Iran and boats trying to lay mines, despite the ceasefire.
Iran's foreign ministry said in a statement that the United States has violated the ceasefire with strikes in Iran's southern Hormozgan province.
Mojtaba Khamenei, 56, succeeded his father, Ali Khamenei, who was assassinated in the opening US-Israel strikes of February 28, triggering retaliatory attacks by Tehran across the region.