Washington: Iran and the United States have attacked each other's behaviour regarding the 2015 nuclear deal as America's top diplomat and Iran's supreme leader traded accusations of backsliding on agreed-to commitments.

Secretary of State Rex Tillerson acknowledged Iran is in "technical compliance" with its obligations under the pact negotiated by the Obama administration and five other world powers. But he faulted Tehran for its non-nuclear activities in the Middle East - backing militias in Yemen and Syria, support for terrorist groups and ballistic missile testing.

Iranian supreme leader, Supreme Leader Ayatollah Ali Khamenei speaks at a meeting in Tehran, Iran, on September 12. Credit:AP

"We have a lot of issues with Iran," he said on CBS' Face the Nation. "They're a yard long. The nuclear issue is one foot of that yard. We have two feet of other issues that we must deal with. And it has to do with Iran's destabilising activities."

For his part, Supreme Leader Ali Khamenei, the ultimate power in Tehran's theocracy, took to his English-language Twitter account to label Washington as, in turn, domineering, bullying, oppressive, hounding and cruel - and corrupt and lying to boot.