But Iran also wants sanctions lifted "on the first day" of the final deal's implementation, against US wishes.
Iranian and US officials have been trying to persuade hardliners in both countries to back the deal.
The deal stipulates Iran must slash its stockpile of enriched uranium that could be used in a nuclear weapon, and cut by more than two-thirds the number of centrifuges that could be used to make more.
In return, UN sanctions and separate measures imposed unilaterally by the US and EU will be lifted as the global nuclear watchdog, the International Atomic Energy Agency (IAEA), confirms Iranian compliance.
In a statement on his website, Mr Khamenei said "it is possible that the untrustworthy side [the six world powers who negotiated the agreement] wants to restrict our country in the details".
Hours after the #talks, Americans offered a fact sheet that most of it was contrary to what was agreed.They always deceive &breach promises.— Khamenei.ir (@khamenei_ir) 9 Aprile 2015