The two leaders, however, asserted confidence that diplomatic tactics will prevail.
Bush said he and Koizumi view the nuclear crisis in "exactly the same way" — an absolute unwillingness to let Pyongyang become a nuclear-armed power.
"We will not tolerate nuclear weapons in North Korea," Bush said in a joint appearance with Koizumi after a summit at his Texas ranch.
"We will not give in to blackmail," Bush said. "We will not settle for anything less than the complete, verifiable and irreversible elimination of North Korea's nuclear weapons program."
"We are confident that our diplomatic approach will bring a peaceful solution," Bush said. "Yet we agreed that further escalation of the situation by North Korea will require tougher measures from the international community."
Koizumi echoed Bush's demands — in some instances using precisely the same language.
"North Korea will have to understand that threats and intimations have no meaning whatsoever," the Japanese leader said.
In a summit that stretched from Thursday afternoon and an intimate dinner, to a ranch tour and business meetings on Friday, the two leaders also discussed their countries' ailing economies, rebuilding Iraq and Afghanistan, and with the United States' development of ballistic missile defense systems.
North Korea has withdrawn from the Nuclear Nonproliferation Treaty and taken steps to restart nuclear facilities it had agreed to freeze under a 1994 agreement.
The White House has been working methodically to line up tough statements from North Korea's neighbors — and got just that from Koizumi. The tough line was similar to that taken earlier this month when Bush met at the White House with South Korean President Roh Moo-hyun.
But neither Bush nor Koizumi elaborated on the "tougher measures" both promised. The United States has repeatedly refused to rule out military strikes on North Korea and, short of that, has considered strengthening U.S. military forces in the area.
As a country listed by the State Department as a state sponsor of terrorism, North Korea is barred from receiving U.S. arms-related exports, economic assistance and U.S. support for loans by the World Bank and other international financial institutions.
The administration has said it has no plans to provide economic benefits to North Korea until the country dismantles its nuclear weapons programs.
The United States has provided hundreds of thousands of tons of food aid to North Korea since the mid-1990s. The Bush administration has said that assistance will continue, given the gravity of the food shortage there.
Koizumi, meanwhile, said his country "will crack down more vigorously on illegal activities" by North Korea, an apparent reference to Pyongyang's suspected drug trade and illegal missile exports.
The two leaders also agreed that future talks should include Japan and South Korea and, Bush said, "at some time later perhaps others."
"Coordination among Japan, the United States and the Republic of Korea is crucial" to a peaceful solution, Koizumi said.
At talks in Beijing, North Korea said it would give up its nuclear and missile programs in exchange for economic aid and security guarantees.
Before they spoke, the foreign ministers of Group of Eight countries meeting in Paris issued a statement urging North Korea to begin the "full, prompt, verifiable and irreversible dismantlement" of its nuclear program, and suggested that the talks started in Beijing in April also include South Korea, Japan and Russia.
Koizumi got what he wanted out of the meeting as well, obtaining Bush's backing in accounting for Japanese nationals abducted by North Korea in the late 1970s and early 1980s. Japan has said that ties with North Korea can never be normalized without that issue being settled.
"I assured the prime minister that the United States will stand squarely with Japan until all Japanese citizens kidnapped by North Korea are fully accounted for," Bush said. "I strongly condemn the kidnapping of Japanese citizens by the North Koreans."
By Scott Lindlaw