Mr Koizumi is on a farewell North American tour before he stands down in September and both leaders stressed the close relationship they have built up over the past five years.
Mr Bush told a press conference, "Today we talked about North Korea, Iran and Iraq, and trade, and energy cooperation.
"It's an amazing fact that we are able to have these discussions. To me it shows the power of liberty and democracy to transform enemies to allies," he said referring to the years during World War Two when the US and Japan were enemies.
Mr Bush said that Washington and Tokyo wanted to send "a clear message" to North Korean leader Kim Jong-Il over the Stalinist state's nuclear weapons and reported plans to launch a long range missile.
"We discussed this issue at length. We both agree that it's important for us to remain united in sending a clear message to the North Korean leader that first of all launching the missile is unacceptable."
The US president said Kim "has an obligation" to inform other countries of his plans.
Mr Bush denounced Pyongyang's kidnapping of Japanese nationals to train its spies, an issue extremely emotional in Japan.
Mr Koizumi said different tactics could be used to dissuade North Korea from launching the missile and that "various pressures" would be applied if the missile was fired.
Iran issue grave: Koizumi
Meanwhile, Mr Koizumi called the Iranian nuclear crisis "a grave issue," despite Tokyo's traditionally close ties with Tehran.
The United States has backed a package of incentives crafted with Britain, France, Germany, China and Russia in an effort to convince Iran to limit its nuclear program.
Japan has been a major investor in Iran's energy sector, as it is heavily dependent on Middle Eastern oil.
"The Iranian issue remains a grave issue for the entire world economy. And Japan wishes to cooperate with the United States and other countries concerned on this matter as well," Mr Koizumi said.
However Japanese officials said that the two leaders did not discuss possible sanctions that could be taken against Iran.
Mr Koizumi also declined to give outright support to a controversial US deal to help India develop civilian nuclear facilities, telling Bush that Japan was reviewing the issue.
Respect for the King
In a symbolic joint statement, the two leaders said the US-Japan partnership is "one of the most accomplished bilateral relationships in history."
The bilateral political, economic and military alliance has contributed to stability in Asia-Pacific, the statement said.
Mr Bush joked that the high point of Koizumi's visit would likely be a visit on Friday to the Memphis mansion of the late Elvis Presley.
"Officially, he's here to see the president, but I know the highlight of his visit will be paying his respects to the King," said Mr Bush, who will also go to Memphis in a sign of their friendship.