"We are completely grateful for Egypt's support in the Iranian nuclear deal," Xinhua quoted Kerry as saying at a press conference in Cairo.
"Iran is part of the instability in several countries in the region and the nuclear programme should be peaceful so we can discuss the future of security in the region."
"But there is a fact, that if Iran is a problem, the nuclear weapons disarmament will improve security in the region," he said, adding that Iran has chosen to abide by the deal.
Kerry will travel to Doha later on Sunday to meet his counterparts from the six Gulf Cooperation Council (GCC) member states.
He said that in case of Iranian violation of the deal, all choices will open in the future.
Experts said Kerry's trip, which ends on August 8, came to assure the region, the Gulf countries in particular, over the expansion of the Iranian influence after the nuclear deal was signed on July 14.
On US-Egyptian ties, Kerry said the two countries were returning to a "stronger base" in their relationship despite tensions and concerns over human rights and democracy.
Egypt's Foreign Minister Sameh Shukri said at the joint news conference that his country has "no major disagreements with the United States but there are differences in points of view over some issues, which is natural".
"During the dialogue, we discussed our shared interests in issues related to democracy and human rights, and I affirmed Egypt's commitment to paying attention to these issues as they fulfill the aspirations of the Egyptian people," Shukri said.
Kerry's visit comes days after the US released its first delivery of F-16 warplanes to Egypt.
"The American people are committed to the security and economic well-being of the Egyptian people," Kerry said.