WASHINGTON — President Bush, in what amounts to a flinch following North Korea’s test of a nuclear explosive, is telling the communist nation that if it shares its nuclear material or know-how with its fellow member of the “axis of evil,” Iran, it must face dire consequences.

“The transfer of nuclear weapons or material by North Korea to states or nonstate entities would be considered a grave threat to the United States, and we would hold North Korea fully accountable of the consequences of such action,” Mr. Bush said in response to the Pyongyang regime’s purported nuclear test yesterday, after citing North Korea’s transfer of long-range missiles to Syria and Iran.

There was skepticism yesterday about Pyongyang’s claim. U.S. officials and other experts said the explosion was smaller than expected, the Associated Press reported, and the Washington Times is reporting today that American intelligence agencies are indicating that the blast was too small to be nuclear, according to the Drudge Report. Russia was the only country to say it had “no doubts” over the North Korean claim, the AP said.

Mr. Bush’s warning, though tepid in the context of the warnings issued by the communist nation before the blast, won quick support in the Senate. “North Korea’s threatening behavior will not be tolerated by the United States,” he said yesterday in a statement. “North Korea is not only exploring missile technology but also transferring that technology to Iran and possibly Syria,” Senator Santorum of Pennsylvania, who is the third ranking Republican in the Senate, said.

Over the last year, the intelligence community has fiercely debated potential nuclear cooperation between Pyongyang and Tehran, administration officials said yesterday. Some analysts confirmed reports in the British and German press last October and December that North Korean engineers arrived in Iran in 2005 to help construct underground enrichment facilities. Others point out that North Korea has built its bomb in Yongbyon largely through plutonium, while the Iranians have sought to enrich uranium.

What is not disputed is the level of cooperation on conventional and ballistic weapons between the two countries. In July, two Iranian engineers were on hand to witness North Korea’s failed test of a multi-staged missile. During the Iran-Iraq war, North Korea provided Iran with tanks and most of its artillery ammunition. The American intelligence community also believes that the nuclear programs of both North Korea and Iran were accelerated with the help of a Pakistani scientist, A. Q. Khan, whose involvement was disclosed after the deal Britain and America forged with Libya in 2003.

Iranian Shahab missiles are closely based on a North Korean design. North Korea is widely believed to have traded with Pakistan designs of its short-range missiles in exchange for nuclear expertise. President Musharraf disputes this account in a memoir published last month. The president’s threat was also well received in the House. The chairman of the House subcommittee that oversees Middle East affairs, Rep. Ileana Ros-Lehtinen, a Republican of Florida, called for a formal investigation into which countries contributed to the North Korean program and which countries have received North Korean nuclear assistance.

Ms. Ros-Lehtinen’s Democratic colleagues, however, could not resist making a political point, stressing how the purported test Sunday reflected a failure in President Bush’s attempt to defuse North Korea’s nuclear program by multilateral diplomacy. Speaking at a Columbus Day parade in New York, Senator Clinton, a Democrat of New York, said, “This really raises serious questions about the Bush foreign policy. You know, six years ago, the North Koreans did not have a nuclear weapon; they did not have a missile capable of delivering a nuclear weapon to our allies in the region like Japan, or to Hawaii, or the West Coast of the United States. The Bush administration’s policies with respect to North Korean are a failure.”

North Korea announced in 2002, when President Clinton was in office, that it was working on making nuclear material at a time when America was in direct negotiations with Pyongyang. In 1998, North Korea tested a Taepodong missile over the Sea of Japan.

Senator Schumer, also a Democrat of New York, struck a different note. He praised Mr. Bush’s response yesterday as “sober, somber, appropriate.” Calling the test the most dangerous moment for America since September 11, 2001, Mr. Schumer also warned of a possible transfer of nuclear material and knowledge. “The great danger that North Korea poses to us with its nuclear capability is not that they’ll fire a missile at us — they don’t have that capability — but rather that they will give these weapons to a terrorist group who will smuggle it into our country and god forbid explode it,” he said. One criticism heard among Democrats yesterday is that Mr. Bush’s decision to group North Korea in an “axis of evil” with Iran may have inadvertently spurred the two countries to cooperate. A former senior State Department official under President Clinton, Lee Feinstein, yesterday said he did not have specific knowledge about North Korean and Iranian nuclear cooperation but nonetheless believed the possibility to be a serious risk.

“I don’t know specifically,” he said. “But it’s a genuine a concern. Outliers are tempted to cooperate. This has to be a concern. North Korea’s nuclear capacities are not the same as they were yesterday.”

The former George W. Bush speechwriter credited with helping coin the phrase “axis of evil,” David Frum, yesterday said many have misinterpreted the phrase to suggest that Iran and North Korea were formal allies. “The reason for the word axis was not because they were allies,” he said. “Germany and Japan were not allies, but opportunistic collaborators against the United States.” Mr. Frum added that that this collaboration between Iran, North Korea, and other states like China and Pakistan had been percolating for several years.