"I don't think we're seeking to go to war with Iran, and I don't think that's what we're focused on," General Joseph Votel, who heads the US Central Command, told Pentagon reporters.

His comments came the day after Secretary of State Mike Pompeo said the US was terminating a 1955 friendship treaty with Iran reached under its pro-Western shah.

And President Donald Trump's national security advisor John Bolton, a longtime mega-hawk on Iran, last week said the US would maintain a presence in Syria even after the Islamic State group has been defeated.

"We're not going to leave (Syria) as long as Iranian troops are outside Iranian borders," Bolton said.

"That includes Iranian proxies and militias," he added, going on to warn of Tehran of "hell to pay" if it threatens the US or its allies.

"Let my message today be clear: we are watching, and we will come after you."

James Jeffrey, the US special representative on Syria, later said a continued US presence in the war-torn country did not necessarily mean American boots on the ground.

Votel has not been given any "direct military tasks" in terms of the pressure campaign being waged by the Trump administration, but he said the Pentagon remains "prepared to respond rapidly massively if the situation requires."

The Trump administration, which is close to Iran's rivals Saudi Arabia and Israel, has withdrawn from a deal to curb Iran's nuclear program and vowed to challenge Tehran's influence in Syria as well as Yemen and Iraq.

Trump has been clear the Iranian regime needs to "cease its destabilizing behavior and policy that spreads violence and human misery throughout the Middle East," Votel said.

"The principle way that we are approaching that right now is through diplomatic and economic pressure. And I support that, I don't see that necessarily as being on the road to war with Iran."