Taro Aso, the Japanese foreign minister, said there was a "very high possibility" that it would impose economic sanctions on North Korea, while the Japanese embassy in Beijing said the launch was "a grave problem" for Japan's security.
In Washington, the White House press secretary said the US "strongly condemned" the missile launches and North Korea's "unwillingness to heed calls for restraint from the international community".
"We are consulting with international partners on next steps," Tony Snow said.
Nato called for a "firm response" from the UN Security Council to North Korea's actions.
However, China called on all sides to "remain calm and exercise restraint" after the tests, saying it hoped that all sides would "refrain from actions that will increase tensions and complicate the situation".
The US said a long-range missile fired during the tests on Tuesday was thought to be a Taepodong-2, but it failed about 35 seconds after launch. At least five more short-range missiles were fired, but, according to Russian and South Korean sources, it may have been as many as nine.
After the initial barrage another missile was fired about 12 hours later that was either a short- or medium-range weapon, Japanese and South Korean military and media sources said.
"North Korea must stop provocative activity, immediately return to six-party talks and join international efforts for nuclear non-proliferation"
Suh Choo-Suk, South Korean security policy adviser
In Russia, the foreign ministry expressed "regret" at North Korea's action and said that it had not been given advanced warning of the tests.
It said in a statement: "Such actions definitely do not aid in strengthening stability and mutual understanding in the region.
"Such actions significantly complicate the situation surrounding the Korean nuclear programme."
South Korea also condemned the tests.
Suh Choo-Suk, security policy adviser to Roh Noo-Hyun, the South Korean president, said: "North Korea must stop provocative activity, immediately return to six-party talks and join international efforts for nuclear non-proliferation."
The UN Security Council is to meet on Wednesday to discuss the tests at the request of the Japanese mission to the UN, which is expected to present a resolution condemning the launches, diplomats said.
The Taepodong-2 is said to be capable of travelling up to 4,300km, which could put parts of the US state of Alaska in range.
George Bush, the US president, and Junichiro Koizumi, the Japanese prime minister, had warned North Korea against test-firing a long-range missile.
Bush had warned North Korea not
to test fire a long-range missile
Last week, Bush spoke of a harsh US response if North Korea went ahead with such a launch.
North Korea, one of the world's most politically isolated countries, last test-fired a Taepodong missile in 1998.
The country has so far not made any public comment on the tests.