"The solution to this issue serves the interests of all countries in the region. It is not at the expense of any state in the region," Zarif said after meeting Kuwaiti counterpart Sheikh Sabah Khaled al-Sabah.
"Be assured that the nuclear deal is in favour of the stability and security of the region," Zarif said in his first official visit to a Gulf Arab nation.
The Islamic republic last Sunday struck a landmark deal in Geneva with Western powers on Iran's disputed nuclear programme.
The Geneva deal was welcomed by the Sunni-ruled Gulf Arab states, which have long been concerned about Shiite Iran's regional ambitions.
Relations between the six Gulf Cooperation Council (GCC) nations and Tehran have deteriorated further because of Iran's support for Syria's President Bashar al-Assad.
After his election, Iran's President Hassan Rouhani said he hoped to improve relations with neighbouring countries, especially Gulf states.
Zarif said in Kuwait City that Iran was looking to open a new page in relations with the Gulf.
"We look at Saudi Arabia as an important and influential country in the region," he said.
Zarif said the Geneva deal does not satisfy all of Iran's demands or "the goals of the other party, but it is important to implement it".
"We will implement the deal and are convinced that implementing it will build the trust," he said.
