Santiago, Chile ? On his first trip overseas since winning re-election, President Bush on Saturday stepped up the pressure on Iran and North Korea, whose nuclear threats critics accused him of neglecting in his first term.

Bush saved his harshest words for Tehran, seizing on new allegations that the Iranians are proceeding with the production of a gas used in the production of nuclear bombs despite pledging to halt such activity under a tentative accord with European nations.

“We’re concerned about reports that show that they’re willing to speed up processing of materials that could lead to a nuclear weapon,” Bush said as he began two days of meetings at the annual Asia-Pacific Economic Cooperation summit here.

Bush was referring to allegations leveled late last week in news reports that Iran, despite its assurances to the contrary, is producing large amounts of a gas used to enrich uranium. Earlier in the week, Secretary of State Colin L. Powell charged that Tehran is working on a missile system to deliver a nuclear bomb. Iran claims its nuclear program is for peaceful, civilian purposes.

On the topic of North Korea, Bush proclaimed that the five nations involved in discussions with the Pyongyang regime will speak with a “common voice” in the quest to rid the North of its nuclear arsenal.

“I can report to you, having visited with the other nations involved in that collaborative effort, that the will is strong,” the president told Pacific Rim business leaders after huddling separately with the leaders of China, South Korea, Japan and Russia, all participants in the so-called six-party talks with North Korea. “The effort is united. And the message is clear to Mr. Kim Jong Il: Get rid of your nuclear weapons programs.”

The president told reporters that North Korea should understand “that the six-party talks are — will be — the framework in which we continue to discuss the mutual goal we all have, which is to rid the Korean peninsula of nuclear weapons.”

Bush’s mantra of unity among the nations comes as some allies have expressed concern that the U.S. administration will take a harder line in its standoff with North Korea in the wake of Bush’s re-election. Earlier this month, South Korean President Roh Moo-hyun appeared to call for greater flexibility in the approach to Pyongyang.

But on Saturday, a U.S. official said Roh’s speech did not come up during his session with Bush and that the two leaders found common ground.

“They both agreed that the situation was complex and . . . that together they had built the approach and it was the six-party talks,” said the official, who declined to be named.

North Korea and Iran are the two remaining pillars of what he once dubbed the “axis of evil” now that Iraq’s Saddam Hussein has been overthrown. Bush’s focus on the nuclear threat they may pose comes after a re-election campaign in which the 2001 terrorist attacks, the Iraq invasion and economic concerns overshadowed what some administration critics said should have been a far more pressing concern.

Now, as Bush seeks to balance the complicated diplomacy of an Iraq war unpopular with many U.S. allies with the need to show unity in confronting Tehran and Pyongyang, the nuclear threat could prove a defining issue of his second term.

“It’s time for the real world to come back into play,” said Ralph Cossa, president of the Pacific Forum, a security think tank. “There are few items more pressing than the nuclear issue.”

During the campaign, Democratic presidential nominee John F. Kerry criticized Bush for neglecting the issue by refusing to negotiate directly with North Korea one-on-one. White House officials favored the multiparty approach, which they said would prevent North Korea from misleading individual negotiators and playing nations off each other.

In the past, the Bush administration has sought to isolate North Korea, rejecting the Clinton strategy of offering incentives for Pyongyang to abandon its nuclear program. But some participants in the six-party talks, such as China and South Korea, support concessions to woo North Korea.

North Korea abandoned the six-party talks last summer. U.S. officials believe the move was an attempt to stall negotiations until after the U.S. presidential election, when Pyongyang might have been dealing with a presumably less hard-line Kerry administration.

A U.S. official said all the participants who met with Bush on Saturday were optimistic that North Korea would rejoin the talks, but it was not clear when that might happen.

Intelligence experts believe that North Korea has enough material to construct between four and eight nuclear bombs. U.S. officials believe Iran is building a system to deliver a nuclear weapon.

Powell’s allegations about the missiles came as a surprise to British, French and German negotiators, who have been assured by Tehran that Iran is not building such a delivery system. Inspectors from the International Atomic Energy Agency have yet to find evidence that Iran is producing weapons.

Powell contended Saturday that other countries and groups in the international community have come around to the U.S. way of thinking about the Iranian nuclear program.

“We have maintained for four years that the international community should be concerned about Iran’s activities with respect to its nuclear program,” Powell said.

He noted that in the fall of 2003, the three major European powers — Britain, France and Germany — had reached agreement with Iran, “which it then walked away from in the course of 2004.” He noted again that Iran has been working for years on long-range missiles, and “when you see what they have been doing over the years with missiles and potential delivery systems, it is a cause of concern.”

There were signs Saturday that the mixed signals on Iran coming from Washington and its European allies could be a strategy of sorts — at least, according to remarks made by Deputy Secretary of State Richard Armitage to the Arabic-language television network Al-Jazeera.

“My view would be that the incentives of the Europeans only work against the backdrop of the United States being strong and firm on this issue,” Armitage said. “In the vernacular, it’s kind of a good cop-bad cop arrangement. If it works, we’ll all have been successful.”

Also Saturday, Bush and Russian President Vladimir V. Putin discussed Putin’s recent moves to re-centralize power in the Kremlin.

The official said that Bush questioned Putin, and the Russian leader reached back to the Stalinist era to explain his country’s unique situation as a “multiethnic society on a large landmass.”

It was the first time Bush and Putin had discussed the matter in person, but it appeared the two leaders reached little understanding.

“There was a lot of back and forth, the president asking questions, underscoring his concerns and wanting to know exactly how this would move forward to, or help develop a democratic Russia,” the administration official said. “We’ve laid the basis for further discussions of this as we move forward.”