Obama spoke alongside French President Francois Hollande a week after a large French business delegation travelled to Tehran to test opportunities that could be opened by the easing of Western sanctions.
"Businesses may be exploring -- are there some possibilities to get in sooner rather than later if and when there is an actual agreement to be had?" Obama said.
"But I can tell you that they do so at their own peril right now. Because we will come down on them like a ton of bricks."
"Sanctions will only be lifted if and when there is definite agreement," Hollande said.
"During this period of the interim agreement, they remain in force."
The 116-strong French delegation, with representatives from major companies like Total, Lafarge and Peugeot, was the largest of its kind from Europe since a landmark nuclear deal reached with the major powers in November gave Iran limited relief from crippling US and EU sanctions.