He also announced that the Syria Support Group of 20 nations and organisations will meet "very shortly" to help push peace in the war-ravaged country.
Kerry spoke in Riyadh after attending a meeting with his Saudi counterpart Adel al-Jubeir and other foreign ministers from the six-nation Gulf Cooperation Council.
"The United States remains concerned about some of the activities that Iran is engaged in in other countries," Kerry told reporters, citing as an example Iran's "support for terrorist groups like Hezbollah".
Those feelings crystallised with the historic international deal which this month lifted crippling economic sanctions on Iran in return for a scaling back of its nuclear capabilities.
Kerry has long sought to reassure his Gulf allies about the overtures to Iran, the world's leading Shiite power whose relations with Sunni rival Saudi Arabia have worsened this month.
Saudi Arabia and some of its allies cut diplomatic ties this month with Iran after protesters there burned Riyadh's embassy in Tehran and a consulate in the second city of Mashhad.
Nimr was one of four Shiites put to death on January 2 alongside 43 Sunnis. All were convicted of "terrorism".
Jubeir told reporters that he did not see a "coming together" of the US and Iran.
"Iran remains the world's chief sponsor of terrorism," Jubeir said. "Overall I think the United States is very aware of the danger of Iran's mischief and nefarious activities... I don't believe the United States is under any illusion as to what type of government Iran is".
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