N Korea faces "tougher measures" if it further escalates the current crisis over its nuclear programme, Japan and the US have said in a joint warning.
Mr Koizumi is on a short visit to Mr Bush's ranch in Texas
After talks with Japanese Prime Minister Junichiro Koizumi at his Texas ranch, US President George Bush said both leaders had agreed they could not give in to "blackmail".
The meeting, at Mr Bush's ranch in Texas, forms part of Washington's strategy of garnering support for its policy towards the renegade state from North Korea's neighbours.
Mr Bush told the joint news conference: "We are confident that our diplomatic approach will bring a peaceful solution.
"Yet we agreed that further escalation of the
situation by North Korea will require tougher measures from the international community."
Neither leader spelt out what the tougher measures might constitute.
Mr Bush added: "The prime minister and I see the problem exactly the same way. We will not tolerate nuclear weapons in North Korea.
"We will not give in to blackmail. We will not settle for anything less than complete, verifiable and irreversible elimination of North Korea's nuclear weapons program."
Last week, Mr Bush met South Korean President Roh Moo-hyun, and the two men issued a statement saying they would not tolerate a nuclear North, and would consider taking "further steps" to prevent it if diplomacy failed.
Japan is also anxious to bring an end to the current impasse. Tokyo feels threatened by nearby Pyongyang's weapons programme, especially since the communist state test-fired a suspected Taepodong-1 missile over Japan's main island of Honshu in 1998.
Analysts say that Seoul has appeared to harden its position on the North's nuclear programme since talks with Washington last week.
The standoff with North Korea began last October, when
Washington accused Pyongyang of admitting to a secret
nuclear weapons programme in violation of a 1994 agreement.
US officials said the North Koreans admitted during talks in Beijing last month that the country already had nuclear weapons, as well as the capability of building more.
At the Beijing talks, North Korea reportedly refused to scrap its nuclear programme unless it received a series of economic and diplomatic concessions from America.