Khamenei, the country's highest authority, said in a statement quoted on his website that Tehran would block any US attempt to influence Iran despite the historic accord.
"They think that through this agreement -- the fate of which is not clear as no one knows if it will be approved here or in America -- they could find a way to intrude into the country," Khamenei said.
"We have closed such a path and will decisively shut it. We'll allow neither economic nor political nor cultural intrusion by the United States."
Khamenei, quoted as speaking to members of the Islamic Radio and Television Union in Tehran, also accused the United States of trying to "infiltrate" the Middle East.
"They seek the disintegration of Syria and Iraq, (but) with God's help it will not happen," he said.
Khamenei's remarks reflected Tehran's continued deep suspicion of the United States, despite his backing President Hassan Rouhani in reaching a deal.
The agreement between Iran and six major powers -- Britain, China, France, Germany, Russia and the United States -- aims to curb Iran's nuclear programme in exchange for a gradual lifting of international sanctions imposed on its economy since 2006.
Obama is likely to veto that measure, but Congress could still override such a veto -- and kill the Iran deal -- with a two-thirds majority in both the Senate and House of Representatives.
In Iran, a debate is ongoing on the need for parliament to approve the agreement.
A majority of lawmakers -- 201 of 290 -- has requested that the agreement be submitted as a bill to be voted on and approved.
Khamenei also stressed his support for all forces fighting Israel, the Islamic republic's arch-foe.
Iran does not recognise Israel and supports the Lebanese Shiite movement Hezbollah and Palestinian Islamist groups Hamas and Islamic Jihad.
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