Obama made the remarks at a joint news conference with French President Francois Hollande, a key partner in both the Syrian and Iranian efforts.
The United States and France are among the countries that signed an interim nuclear agreement with Tehran. The agreement halts progress on the Islamic republic's nuclear program in exchange for easing international sanctions. Talks on a final deal begin next week in Vienna, Austria.
Speaking on companies doing business with Iran in violation of sanctions still in place, Obama said, "We will come down on them like a ton of bricks" if they don't hold up their end.
The Obama administration has objected to the interest French businesses have shown in Iran since the sanctions were eased. More than 100 French executives visited Tehran last week, a trip Secretary of State John Kerry told his counterparts in Paris was "not helpful."
The United States and France have been working to end the civil war in Syria, a former French colony. But peace talks between the Syrian government and opposition forces have gained no traction.
An agreement to strip Syria of its chemical weapons stockpiles is being carried out. But there are concerns on both sides of the Atlantic that Syria is stalling on its obligations.
When Obama threatened a military strike against Syria following a chemical weapons attack there last year, France was the only European ally ready to join that effort.
The United State and France have rebuilt a relationship that "would have been unimaginable even a decade ago," after President George W. Bush launched an unpopular war against Iraq.
Obama said the transformation stands as a testament to how Washington and Paris have worked to transform their alliance, as the two leaders worked to project a renewed relationship between their countries after hitting a low point more than a decade ago over France's staunch opposition to the American-led war in Iraq.
Obama also announced that he's accepted Hollande's invitation to travel to France for the June 6 ceremony marking the 70th anniversary of the D-Day invasion of Normandy.
The remarks came at a news conference in the midst of an official state visit, held as Hollande is facing romantic upheaval that resulted in his showing up stag to the White House. The 59-year-old ended his relationship last month with girlfriend and French first lady Valerie Trierweiler after it was revealed that he was having an affair with an actress.
The White House has carefully avoided any mention of Hollande's personal drama and has moved forward with a grand welcome reserved only for America's closest allies.
On a cold February morning, Obama, first lady Michelle Obama and a military honor guard welcomed Hollande as he arrived on the South Lawn of the White House. The two leaders shook hands before a cheering crowd, many waving American and French flags, and greeted two American military veterans who served in France during World War II.
Following the arrival ceremony, Obama and Hollande held a private meeting in the Oval Office before appearing before the press in the East Room. The Obamas planned to fete Hollande at a grand state dinner Tuesday night attended by more than 300 dignitaries and celebrities.
—By The Associated Press.