In a speech marking the end of the Islamic holy month of Ramadan, he said Iran still had sharp differences with the US, above all over the Middle East.
Iran would continue to back Syria, Iraq, the Palestinians and "oppressed people" in Yemen and Bahrain, he said.
The deal on Iran's nuclear programme came after years of negotiations.
The agreement limits Iran's nuclear activities for at least 10 years in exchange for the gradual lifting of sanctions which have hampered the country's economy.
"Whether the [nuclear] deal is approved or disapproved, we will never stop supporting our friends in the region and the people of Palestine, Yemen, Syria, Iraq, Bahrain and Lebanon," Ayatollah Khamenei said.
"Even after this deal our policy towards the arrogant US will not change."
The supreme leader also denied that Iran was intending to create a nuclear bomb.
"The Americans say they stopped Iran from acquiring a nuclear weapon," he said in his speech at the Mosala mosque in Tehran.
"They know it's not true. We had a fatwa [religious ruling] declaring nuclear weapons to be religiously forbidden under Islamic law. It had nothing to do with the nuclear talks.
"We have repeatedly said we don't negotiate with the US on regional or international affairs; not even on bilateral issues.
"There are some exceptions like the nuclear programme that we negotiated with Americans to serve our interests... US policies in the region are diametrically opposed with Iran's policies."
The supreme leader said it was now necessary for Iranian politicians to scrutinise the nuclear agreement and make sure that Iran's national interests were being preserved.
Correspondents say that Ayatollah Khamenei's views are in contrast to the acclaim that the accord has received from President Hassan Rouhani and Foreign Minister Mohammad Javad Zarif.

Jim McCafferty, 71, appeared before Belfast Magistrates' Court charged with eight counts of touching a boy under the age of 16.
The crimes are alleged to have happened in Belfast between 2012 and 2015.
Mr McCafferty, who previously lived in Glasgow and worked at Celtic more than 20 years ago,  was arrested last December.
He was also a kit man for other Scottish clubs, including Falkirk and Hibernian, before moving to Northern Ireland about seven years ago.
Mr McCafferty, who now has an address at Raby Street in south Belfast, has been on remand at Maghaberry Prison amid fears for his safety.
He was escorted into the dock on a walking frame for the hearing at Belfast Magistrates' Court on Thursday.
Dressed in a white T-shirt and and grey tracksuit bottoms, the pensioner spoke to confirm he understood the allegations against him.
The judge ordered his trial to be held at Belfast Crown Court on a date to be fixed.
No application for bail was made and he is expected to remain in custody until the proceedings get underway.
Iran's stance towards the "arrogant" US will not change despite the nuclear deal reached earlier this week, supreme leader Ayatollah Ali Khamenei has said.
[NEXT_CONCEPT]
A former Celtic Football Club youth coach and kit man is to stand trial for alleged child sex offences.