His remarks signaled that Tehran will not agree to dismantle any of its atomic facilities in talks with six world powers on a final settlement of the decade-old dispute over its nuclear activity.
Those negotiations got under way in Vienna last week, with both sides saying they made a "good start" but conceding that their plan to achieve a long-term deal in the coming months was very ambitious.
By late July, Western governments hope to hammer out an accord that would lay to rest their suspicions that Iran is seeking the capability to make a nuclear bomb, an aim it denies, while Tehran wants a lifting of economic sanctions.
Zarif, speaking to reporters during a visit to New Delhi, said he hoped a deal would be reached by the July deadline, although talks could be extended by another half year if both sides agreed.
"I am hoping by the first deadline we will reach a final deal and to start implementing it," he said. "And I can assure you that Iran has that political will and good faith that is required in order to achieve that."
However, he also said there was a "problem in terms of both substance and approach", apparently referring to the other side in the talks.
Iran and the powers - the United States, Russia, France, Germany, China and Britain - aim to build on an interim accord reached in November under which Tehran curbed its most sensitive nuclear work, higher-grade uranium enrichment, in exchange for some sanctions easing.
Diplomats and analysts acknowledge that it probably will be even more difficult to reach a final agreement as the Western powers would likely press for a significant scaling back of Iran's nuclear program, including of the number of centrifuges that it uses to refine uranium.
Iran says it is enriching uranium to low levels for a planned network of nuclear power plants. But uranium can also be used to assemble bombs if refined further to a high fissile concentration, which the West fears may be Iran's ultimate aim.
U.S. officials have made clear Iran's planned Arak heavy water reactor - which could yield bomb-grade plutonium once operational - must be dealt with under any settlement and Washington has also questioned Iran's need to have a uranium enrichment site buried deep underground at Fordow.
Zarif said Iran was "prepared to make sure that the program is exclusively peaceful and create the necessary understanding for the West. I believe there are multiple ways of doing that and we are willing to entertain those ways."
But, he added: "I can tell you that Iran's nuclear program will remain intact. We will not close any program."
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