In a letter to President Hassan Rouhani, the Leader ordered the July 14 Joint Comprehensive Plan of Action (JCPOA) to be implemented, subject to certain security conditions the Iranian parliament stipulated in a law passed last week.
The Leader said Iran would stop implementing it if the six powers - the United States, Britain, France, Germany China and Russia - imposed any new sanctions.
"Any comments suggesting the sanctions structure will remain in place or new sanctions will be imposed, at any level and under any pretext, would be considered by Iran a violation of the deal,” Ayatollah Khamenei said in the letter.
The Leader said implementation of the deal should be "tightly controlled and monitored" because of some "ambiguities" in it.
"Lack of tight control could bring significant damage for the present and the future of the country," Ayatollah Khamenei said.
The U.S. and EU took formal legal steps on Sunday that will rescind sanctions once Iran meets certain conditions such as reducing the number of centrifuges used to enrich uranium, and its enriched-uranium stockpile.
Another condition will be a resolution of a UN nuclear agency inquiry into "possible military dimensions (PMD)" to the program as the agency terms it.
On that point, Ayatollah Khamenei said that until UN inspectors settled the PMD issue, Iran should delay sending its stockpile of enriched uranium abroad and reconfiguring a heavy water reactor in Arak.
The International Atomic Energy Agency finished collecting samples from Iran's Parchin military complex earlier this month and is expected to announce its conclusions on PMD by Dec. 15.
"Any action regarding Arak (reactor) and dispatching uranium abroad ... will take place after the PMD file is closed," Ayatollah Khamenei said in the letter.
Iran agreed with the powers to fill the Arak reactor's core with concrete so that it could not yield plutonium.
Iran is also required to export more than 90% of its refined uranium stocks, keeping just 300 kg of the material enriched to 3.67% fissile purity - suitable for running civilian nuclear power plants - for 15 years.
Ayatollah Khamenei said U.S. President Barack Obama had sent him two letters pledging America had no intention of toppling the Islamic Republic.
"But this was soon proved a lie ... Neither on the nuclear issue nor in any other cases has America taken any position except hostility and trouble (towards Iran). Therefore any change in the future is unlikely," The Leader’s statement read.
The agreement has been the subject of fierce debate within Iran, with critics arguing that the negotiators gave up too much ground.  
Iran's parliament approved the deal in two stormy sessions that saw lawmakers shout at one another and at least one parliamentarian burst into tears. Iran's Guardian Council ratified the bill a week ago, marking the last legal step for official approval.
But Ayatollah Khamenei warned that the agreement "suffers from multiple structural weaknesses and ambiguous points that can lead to present and future great harms to the country in the absence of precise and constant vigilance".