ASHINGTON, April 5 — Shortly after Defense Secretary Donald H. Rumsfeld issued a stark warning to Iran and Syria last week, declaring that any "hostile acts" they committed on behalf of Iraq might prompt severe consequences, one of President Bush's closest aides stepped into the Oval Office to warn him that his unpredictable defense secretary had just raised the specter of a broader confrontation.

Mr. Bush smiled a moment at the latest example of Mr. Rumsfeld's brazenness, recalled the aide. Then he said one word — "Good" — and went back to work.

It was a small but telling moment on the sidelines of the war. For a year now, the president and many in his team have privately described the confrontation with Saddam Hussein as something of a demonstration conflict, an experiment in forcible disarmament. It is also the first war conducted under a new national security strategy, which explicitly calls for intervening before a potential enemy can strike.

Mr. Bush's aides insist they have no intention of making Iraq the first of a series of preventive wars. Diplomacy, they argue, can persuade North Korea to give up its nuclear weapons programs. Intensive inspections can flush out a similar nuclear program in Iran. Threats and incentives can prevent Syria from sponsoring terrorism or fueling a guerrilla movement in Iraq.

Yet this week, as images of American forces closing in on Baghdad played on television screens, some of Mr. Bush's top aides insisted they were seeing evidence that leaders in North Korea and Iran, but not Syria, might be getting their point.

"Iraq is not just about Iraq," a senior administration official who played a crucial role in putting the strategy together said in an interview last week. It was "a unique case," the official said. But in Mr. Bush's mind, the official added, "It is of a type."

In fact, some administration officials are talking about the lessons Mr. Bush expects the world to take from this conflict, and they are debating about where he may decide to focus when it is over.

The president seemed to allude to those lessons in his radio address this morning, saying his decision to oust Mr. Hussein was part of his plan to "not sit and wait, leaving enemies free to plot another Sept. 11 — this time, perhaps, with chemical, biological or nuclear terror."

But how to turn that broad principle into policy is already emerging as the next fault line in the administration, as well as in its relationships with the nations it alienated on the way to the Iraq conflict.

Some hawks inside the administration are convinced that Iraq will serve as a cautionary example of what can happen to other states that refuse to abandon their programs to build weapons of mass destruction, an argument that John R. Bolton, the under secretary of state for arms control and international security, has made several times recently.

The administration's more pragmatic wing fears that the war's lesson will be just the opposite: that the best way to avoid American military action is to build a fearsome arsenal quickly and make the cost of conflict too high for Washington.

Secretary of State Colin L. Powell has been the most vocal in insisting that Iraq is about Iraq and nothing more. "I think it's a bit of an overstatement to say that now this one's pocketed, on to the next place," he said as the war began.

But Mr. Powell was taken aback — not for the first time — by Mr. Rumsfeld's comments about Iran and Syria. A senior aide said Mr. Powell had cautioned the administration against any public talk of a "domino effect," fearing it would further inflame Arab governments and fuel North Korea's considerable insecurities.

"His view is that we've made enough enemies in the past five months, and we don't need to go looking for another fight," one of his senior advisers said.

In fact, only Mr. Rumsfeld seems willing to name potential adversaries these days. But several senior administration officials, speaking on the condition of anonymity, said they saw signs that some countries were reconsidering their behavior.

Their newest is North Korea, which Gary Samore, the nonproliferation specialist in the Clinton White House, recently called "the dog that hasn't barked."

North Korea's diplomatic broadsides at the United States have been toned down in recent days. No one has seen Kim Jong Il, the country's reclusive leader, in months, and some experts say they believe he may be staying out of sight for fear of his own personal security. So far, at least, the country has not made good on its threat to restart a plutonium reprocessing facility that has the capacity to to produce fuel for a half-dozen nuclear bombs this year. American intelligence agencies had expected him to do so by now.

"He may have simply encountered technical troubles," said one North Korea expert in the administration. "But he may also be looking at CNN and considering the wisdom of his next move. The fact is, We don't know."

Another possible factor, Mr. Bush's aides say, is that China, which is North Korea's main supplier of oil, has finally begun to deliver tough messages to Mr. Kim's government.

Iran may also be newly cautious, the administration argues. After Mr. Rumsfeld issued his warning on March 28 that the United States would not tolerate the entry into Iraq of the Badr Corps — which he said was "trained, equipped and directed by Iran's Islamic Revolutionary Guard" — the incursion was apparently cut off.

Syria is a very different case. In an interview published this week in a pro-Syrian Lebanese newspaper, Bashar al-Assad, Syria's 36-year old president, who inherited the post from his father three years ago, said the war only proved that Mr. Bush "wanted oil and wanted to redraw the map of the region in accordance with the Israeli interests." He urged Arabs to learn from Lebanon's history of "resistance."

Stephen P. Cohen, the Middle East specialist at Institute for Middle East Peace and Development in New York, said: "The Arabs understand that this war is happening at two levels — on the ground in Iraq, and then an ideological war once the ground war is over. They know how the first one is going to turn out, and they are debating how to wage the second."

Mr. Assad seemed to suggest in his interview that Syria would be a new target for Mr. Bush, because it "is the heart of Arabism."

Mr. Bush's national security advisor, Condoleezza Rice, not surprisingly, describes the agenda very differently. "You don't treat every case with the identical remedy," she said today. Even when the problem appears the same — weapons of mass destruction that could be passed to rogue states or terrorists — "there are lots of ways" to accomplish the president's goals, she said

"In North Korea, we're dealing with the issue in one particular way; with Iran, we're dealing with it in other ways," she added. But she also noted the president's belief that there is "a positive agenda for moving forward that could be catalyzed by Iraq."