"Kasuri appreciated the assistance that Japan has given for the stability and for economic development and reconstruction in Afghanistan," the official said of the talks.
The two sides also held talks on North Korea, which is locked in a stand-off with much of the world over its ambitions to build nuclear weapons.
Kasuri said Pakistan "fully appreciates the concerns on North Korea", the official said.
Kasuri and Machimura also discussed proposals to enlarge the UN Security Council.
The Pakistani embassy issued a statement stressing that the issue did not come up in the talks with Koizumi.
In discussions earlier with Japan's main opposition leader Katsuya Okada, Kasuri "highlighted the importance of evolving and objective criteria" in the Security Council and "building a consensus on the issue of Security Council expansion," the statement said.
Kasuri in his meetings also extended an invitation to Koizumi to visit Pakistan and expressed appreciation for Japan's past economic assistance.
Kyodo News reported Saturday that Koizumi was considering visiting India and Pakistan along with Luxembourg and the Netherlands from late April to early May.
Japan has agreed in principle to resume yen loans to Pakistan, which it cut off in 1998 after New Delhi and Islamabad carried out shock nuclear tests.