Kerry spoke during the first stop on his trip to the Middle East, Europe and North Africa.
After Egypt, he headed later Sunday to Saudi Arabia, where the biggest rifts with the Obama administration have emerged.
Saudi officials have complained that the United States did not follow through on its threat to punish Syrian President Bashar Assad with military strikes for his government's use of chemical weapons. The Saudis also have watched warily as President Barack Obama has opened a tentative rapprochement with Iran, Saudi Arabia's archrival.
Kerry acknowledged U.S. divisions with Gulf nations over Syria and Iran, but he played down those differences. He said some countries do differ with U.S. "tactics" in Syria.
"There may some differences on a tactic here and there," he said. But he said they all agree on the goal of ending the fighting and forming an interim government.
"We can have a difference on a policy, on the tactics of the policy," he said. "For instance, there are some countries in the region that wanted the United States to do one thing with respect to Syria and we have done something else."
He stressed, though, that "those differences on an individual tactic on a policy do not create a difference on the fundamental goal of the policy. We all share the same goal that we have discussed, that is the salvation of the state of Syria and a transition government put in place ... that can give the people of Syria the opportunity to choose their future."
Kerry added that that the United States would never allow Iran to obtain nuclear weapons. The administration is seeking a pause from the U.S. Congress in putting in place fresh penalties against Iran, in order to provide flexibility in negotiations.
A new round of nuclear talks between Iran and the five permanent members of the U.N. Security Council and Germany is set to begin Thursday in Geneva.
"Iran will not get a nuclear weapon," he said. "That is a promise by the president of the United States."