(Incorporates IRAN-NUCLEAR/ZARIF)
WASHINGTON, Sept 29 (Reuters) - U.S. Secretary of State John Kerry said a deal on Iran's nuclear weapons program could be reached relatively quickly, and it would have the potential to dramatically improve the relationship between the two countries.
Kerry said intensifying diplomatic efforts to resolve the dispute over Iran's nuclear program could produce an agreement within the three- to six-month time frame that Iranian President Hassan Rouhani has called for.
"It's possible to have a deal sooner than that depending on how forthcoming and clear Iran is prepared to be," Kerry said in an interview aired on CBS's "60 Minutes" on Sunday.
"If it is a peaceful program, and we can all see that - the whole world sees that - the relationship with Iran can change dramatically for the better and it can change fast," he said.
Rouhani and U.S. President Barack Obama spoke by telephone on Friday in the highest-level contact between the two countries in three decades, raising hopes of a breakthrough in Western efforts to prevent Iran from building a nuclear bomb.
The call was the culmination of a recent, dramatic shift in tone between Iran and the United States, which cut diplomatic relations a year after the 1979 Iranian revolution.
Kerry said Iran could prove its sincerity by immediately opening its nuclear facilities to inspections and keeping its uranium enrichment efforts at lower grades that were not suitable for military use.
Iran has defended its right to enrich uranium as part of a civilian nuclear energy and medicine program and denied that it aims to develop atomic weapons, but the United States and its allies have sought an end to higher-grade uranium enrichment that could be a step away from the production of weapons-grade material.
"Iran needs to take rapid steps, clear and convincing steps, to live up to the international community's requirements regarding nuclear programs, peaceful nuclear programs," Kerry said.
"Words are not going to replace actions," he said. "What we need are actions that prove that we and our allies, our friends in the region, can never be threatened by this program."
In a separate interview, Iran's foreign minister said the country's right to peaceful nuclear enrichment was not negotiable but it did not need to enrich uranium to military-grade levels.
Iranian Foreign Minister Mohammad Javad Zarif said Iran was willing to open its nuclear facilities to international inspections as part of a nuclear deal as long as the United States ended painful economic sanctions.
"Negotiations are on the table to discuss various aspects of Iran's enrichment program. Our right to enrich is non-negotiable," Zarif told ABC's "This Week" program.
"We do not need military-grade uranium. That's a certainty and we will not move in that direction," Zarif said. "Having an Iran that does not have nuclear weapons, is not just your goal, it's first and foremost our goal."
Zarif said Iran was willing to have its facilities visited by international inspectors to prove it was not seeking a nuclear bomb.
"If the United States is ready to recognize Iran's rights, to respect Iran's rights and move from that perspective, then we have a real chance," Zarif said.
"We are willing to engage in negotiations. The United States also needs to do things very rapidly. One is to dismantle its illegal sanctions against Iran," he said.
Kerry said the sanctions could be lifted after an agreement was in place that ensured Iran's nuclear program was peaceful.
"The United States is not going to lift the sanctions until it is clear that a very verifiable, accountable, transparent process is in place, whereby we know exactly what Iran is going to be doing with its program," he said. (Reporting by John Whitesides; Editing by Eric Beech and Paul Simao)
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