Kerry, in Saudi Arabia, also said military pressure may be needed to oust Syrian President Bashar al-Assad, who is fighting a civil war against jihadists and Western-backed rebels.
Fresh from three days of negotiations in Switzerland, Kerry gathered at a Riyadh air base with foreign ministers from the six Gulf Cooperation Council nations.
Sunni Gulf states remain wary of a rapprochement between Shiite-dominated Iran and Washington.
"Even as we engage in these discussions with Iran around this programme, we will not take our eye off Iran's destabilising actions in places like Syria, Lebanon, Iraq and the Arabian Peninsula, Yemen particularly," he told reporters in Riyadh.
Kerry said Washington was not seeking a a "grand bargain".
"Nothing will be different the day after this agreement, if we reach one, with respect to any other issues that challenge us in this region, except we will have taken steps to guarantee that Iran will not have a nuclear weapon."
It has also been accused of backing Huthi Shiite militiamen who seized the capital in Saudi Arabia's neighbour, Yemen, and paralysed the Western-backed government.
The nuclear talks in no way represent "a broader warming of ties, lessening of concerns on our part," deputy State Department spokeswoman Marie Harf insisted earlier.
"This is not about a broader rapprochement in any way. This is about the nuclear issue and that's it."
The so-called P5+1 group of Britain, China, France, Russia, the United States and Germany is trying to strike an accord that would prevent Tehran -- Riyadh's regional rival -- from developing a nuclear bomb.
Saudi Arabia and other Gulf nations belong to an international coalition brought together by the US to fight the Islamic State (IS) jihadist group, which has captured swathes of territory in Iraq and Syria.
Riyadh and its neighbours have carried out air strikes against the Sunni extremists.
Saudi Arabia has also agreed to launch with the US a facility for training and equipping vetted members of the moderate Syrian opposition under a long-planned effort to take on IS.
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