"It is intolerable for the peace and the stability in the Middle East if they get a nuclear weapon especially when their stated objective is the destruction of Israel," said Bush.
"The foreign ministers of Great Britain, France and Germany have interceded on behalf of the civilized world to talk plainly to the Iranians," the president told the Newspaper Association of America's annual convention.
"My job is to make sure that they speak as plainly as possible to the Iranians and that they made absolutely clear that the development of a nuclear weapon in Iran is intolerable and a program is intolerable," he said.
The United States has been skeptical of Tehran's pledges to improve its cooperation and transparency with the UN nuclear watchdog, the International Atomic Energy Agency, saying Iran had reneged on similar vows in the past.
Iran last year was severely reprimanded by the IAEA for failing to reveal a full account of its nuclear activities including its research into second generation P2 centrifuges that are capable of enriching uranium to weapons grade.
But last December, Iran bowed to international pressure by signing up to an additional protocol to the nuclear Non-Proliferation Treaty (NPT), allowing a tougher IAEA probe.
"The signing of the additional protocol was a positive element," Bush said.