Deputy national security advisor Ben Rhodes made the comments to reporters accompanying Barack Obama on his visit to Saudi Arabia, during which the US president will be seeking to assure Saudi officials that Washington has not changed its policy on Iran.
"We will be making clear that even as we are pursuing the nuclear agreement with the Iranians, our concern about other Iranian behaviour in the region -- its support for (Syrian President Bashar al-) Assad, its support for (Lebanon's) Hezbollah, its destabilising actions in Yemen and the Gulf -- that those concerns remain constant," said Rhodes.
The interim agreement curbs Iran's controversial nuclear activities in exchange for limited sanctions relief, and is aimed at buying time to negotiate a comprehensive accord.
Analyst Khaled al-Dakhil spoke of "major differences" with Washington, adding that Obama will focus on easing "Saudi fears on Iran and on regional security".
Saudi Arabia, the largest power in the six-nation Gulf Cooperation Council, fears that a possible US withdrawal from the Middle East and a diplomatic overture towards Iran would further feed Tehran's regional ambitions.
"The nuclear talks have the ability of resolving a threat to regional stability; at the same time, we're going to keep the pressure on all those other issues," he said.
The six powers -- Britain, China, France, Russia and the United States plus Germany -- want Iran to reduce permanently, or at least long-term, the scope of its nuclear activities to make it extremely difficult for it ever to develop nuclear weapons.
Iran has always denied any such ambition.
But the icy ties have thawed marginally since President Hassan Rouhani, a moderate, defeated a pool of conservatives in last June's presidential election in Iran after vowing to engage constructively with the West.