WASHINGTON—Iranian President Mahmoud Ahmadinejad said his government would accept a nuclear fuel-swap agreement overseen by the United Nations, a deal the Obama administration has viewed as central to limiting Tehran's ability to develop atomic weapons.

The Iranian leader's announcement on state television Tuesday, however, was immediately greeted with skepticism by Western diplomats, who have watched Tehran flip-flop on the fuel-swap issue since it was proposed in October.

Senior...