The response follows Mr Trump's imposition of new sanctions on Iran over a ballistic missile test.
Mr Trump has also been a fierce critic of the landmark nuclear deal struck between Iran and world powers in 2015.
Mr Khamenei, addressing military commanders in the capital Tehran, said Mr Trump was trying to frighten Iranians, but would fail."We are thankful for this person who has arrived [President Trump]. Our thanks is for making our life easy as he showed the real face of America," he said.
"What we have been saying for more than 30 years about the political, economic, moral and social corruption in the US ruling system, this person arose during the election campaign and... has confirmed it."
US Defence Secretary James Mattis recently called Iran the world's "biggest state sponsor of terrorism".
Iran confirmed last week it had tested a missile but denied violating a UN Security Council resolution on its nuclear activities.
A US statement said Iran's "continued support for terrorism and development of its ballistic missile programme poses a threat to the region".
In a tweet, President Trump accused Iran of playing with fire, adding: "They don't appreciate how 'kind' President Obama was to them. Not me."
