Despite pleas from other parties to the agreement, Trump pulled the US out of the deal in May, claiming the Iranian regime was cheating on its commitments and funding "malign" activities around the region.

"I remain open to reaching a more comprehensive deal that addresses the full range of the regime's malign activities, including its ballistic missile program and its support for terrorism," Trump said in a statement.

A first phase of US sanctions against Iran goes into effect overnight, targeting Iran's access to US banknotes and key industries including cars and carpets.

The second phase, which takes effect November 5 and will block Iran's oil sales, is due to cause more damage, though several countries including China, India and Turkey have indicated they are not willing to entirely cut their Iranian energy purchases.

Trump called the multilateral Iran accord a "horrible, one-sided deal."

It "failed to achieve the fundamental objective of blocking all paths to an Iranian nuclear bomb, and it threw a lifeline of cash to a murderous dictatorship that has continued to spread bloodshed, violence and chaos," he said.

After months of fierce rhetoric, Trump surprised observers last week when he offered to meet with Iranian President Hassan Rouhani without preconditions.

But Iranian Foreign Minister Mohammad Javad Zarif suggested it was hard to imagine negotiating with the man who tore up an agreement on which Iran and world powers had spent the "longest hours in negotiating history."

Trump warned that businesses and individuals that continue to work with Tehran risk "severe" consequences.

"We urge all nations to take such steps to make clear that the Iranian regime faces a choice: either change its threatening, destabilizing behavior and reintegrate with the global economy, or continue down a path of economic isolation," he said.