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 meeting 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” in Lebanon.
Saudi Arabia and its Gulf neighbours perceive a lack of US engagement in the region, particularly in the face of what they see as Iran’s “interference” in Yemen, Syria, Lebanon and elsewhere.
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 calm concerns among 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 with Iran after protesters there burned Riyadh’s embassy in Tehran and a consulate in Mashhad city.
The violence broke out after the kingdom executed dissident Saudi Shiite cleric Nimr al-Nimr, a driving force behind anti-government protests.
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.
“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,” Jubeir added, while Kerry appeared defensive and less at ease than usual.
A senior State Department official earlier told journalists the US understands Saudi anger over the embassy attack but that “lessening tensions is an important objective”.
Iran’s supreme leader Ayatollah Ali Khamenei on Wednesday said violence against the Saudi embassy was wrong, and against Islam.
– Syria peace talks –
Kerry later met with King Salman and the monarch’s son, Deputy Crown Prince Mohammed bin Salman, who is also the defence minister.
He also held talks with Riad Hijab, Riyadh-based general coordinator of Syria’s largest opposition coalition.
UN-brokered peace talks are targeted for Monday in Geneva but there is disagreement, including from Moscow, over opposition representation.
“We are confident that with good initiative in the next day or so those talks can get going,” Kerry said.
On Saturday, he and his Russian counterpart Sergei Lavrov discussed by telephone the makeup of the opposition team.
“Particular attention was given to the need to form a genuinely representative opposition delegation,” a Russian foreign ministry statement said.
Kerry told reporters the Syria Support Group will meet “very shortly” after the first round of Syria talks “because we want to keep the process moving”.
The group has devised a plan for a political transition aimed at ending the nearly five-year war in Syria that has cost more than 260,000 lives and displaced millions.
It includes Saudi Arabia, the United States and other countries who say President Bashar al-Assad can have no role in Syria’s future, and Assad’s allies Iran and Moscow.
Kerry spoke of the “urgency” of ending the conflict but said there are still “obstacles” to finding a political settlement.
“We know it’s tough,” he said.
Saudi Arabia and Iran back opposite sides in the Syria and Yemen wars.
A Saudi-led military coalition since March has been supporting local forces and the internationally recognised government of Yemen against Iran-backed Huthi Shiite rebels.
“We have made it clear that we stand with our friends in Saudi Arabia” on Yemen and the threat from violent Sunni extremism, said Kerry, who travels Sunday to Laos in Southeast Asia.