President Bush gently nudged authoritarian Arab allies yesterday to satisfy frustrated desires for democracy in the Middle East and saved his harshest criticism for Iran, branding it “the world’s leading state-sponsor of terror.” Speaking in this Persian Gulf country, about 150 miles from the shores of Iran, Mr. Bush said Tehran threatens nations everywhere and that America was “rallying friends around the world to confront this danger before it is too late.”

The warning about Iran was much tougher than Mr. Bush’s admonition about spreading democracy in the Middle East, which had been billed as the central theme of his speech.

In a region of autocratic rulers, Mr. Bush did not single out any country for criticism. He spoke about democracy in a deeply undemocratic country, the United Arab Emirates, where an elite of royal rulers makes virtually all the decisions. Large numbers of foreign resident workers have few legal or human rights, including no right to protest working conditions.

“To the people of the Middle East: We hear your cries for justice,” Mr. Bush said. “We share your desire for a free and prosperous future. And as you struggle to find your voice and make your way in this world, the United States will stand with you.”

Usually averse to sightseeing, Mr. Bush rode out into the sand dunes to the desert encampment of Abu Dhabi’s crown prince, Sheik Mohammed Bin Zayed Al Nahyan. He let Mr. Bush hold one of his prize falcons. Later, Mr. Bush returned to his suite in the opulent Emirates Palace Hotel, constructed at a cost of more than $3 billion and reputed to be the most expensive hotel ever built. Meanwhile, a threatening radio message to American warships may have been a coincidence but was taken seriously because it came at the same time Iranian vessels swarmed the American fleet, the commander of one of the American ships said yesterday.

Commander Jeffery James, of the destroyer USS Hopper, and Captain David Adler, of the cruiser USS Port Royal, would not say how close the Navy was to firing at the Iranian ships on January 6 near Iranian waters in the Strait of Hormuz. But the Iranians knew what they were doing when they charged the three American vessels in the Persian Gulf, they said. “This was not a loose bunch of guys,” Commander James said. “During this entire time, we were going through our pre-planned responses trying to warn them off before we had to take any lethal action. And fortunately for everyone involved, they turned outbound before we needed to open fire,” Commander James said.

Also meanwhile, Iran’s leaders agreed to answer all remaining questions about their country’s past nuclear activities within four weeks in talks with the U.N.’s chief nuclear inspector, his spokeswoman said yesterday.

The spokeswoman also said the International Atomic Energy Agency chief, Mohamed ElBaradei, received new information on Iran’s “new generation of centrifuges” — a priority as the agency tries to establish how far advanced Iran is in developing the technology, which could be used in a weapons program.

The four-week deadline is meant to wrap up an IAEA probe of past Iranian nuclear programs. A diplomat familiar with the talks said investigation now was focused on the most delicate aspects of Iran’s past atomic work, including programs linked to American suspicions the country conducted experiments linked to nuclear arms. The probe was originally slated to be completed in December, and America and its allies have been chafing at the delay, diplomats accredited to the IAEA say. But they are unlikely to object publicly if the extension allows Mr. ElBaradei to expose details of such secret programs.

Mr. ElBaradei yesterday ended a two-day visit to Tehran that included unprecedented meetings with both Ayatollah Ali Khamenei, Iran’s supreme leader, and President Amhmadinejad.

A senior diplomat expressed doubt Mr. ElBaradei was able to persuade Iran to freeze enrichment and noted Western efforts for additional U.N. sanctions against Iran would continue unless that condition was met.