French President Jacques Chirac said he regretted an action that started without United Nations backing and predicted it would have "serious consequences."
Indonesian President Megawati Sukarnoputri denounced the attack, and China called it a violation of the U.N. charter.
Officials in Pakistan strongly criticized the strikes, but said Iraqi President Saddam Hussein shared the blame because he did not pursue all possibilities to avoid war.
In cities across Europe, including Athens, Rome, and Paris, thousands of protesters demanded an end to the U.S.-led action. Demonstrators also took to the streets in Jordan, Syria and Egypt.
The BBC reported 100,000 marchers in Athens.
One of the most raucous demonstrations took place in London, where a crowd estimated at 5,000 shut down the streets leading to and from Parliament while police watched from vans and horseback. Another London protest is planned for tomorrow.
Few of the official reactions were unexpected, given past public opposition by various governments. And other nations - including Australia, Japan and New Zealand - expressed expected support.
South Korean President Roh Moo Hyun said yesterday that military action in Iraq was unavoidable and that his country would support the war effort by dispatching noncombat troops. He also said he would try to make sure the conflict didn't lead to a worsening of relations with North Korea.
But widespread anger over the war could affect international support as the world is called upon to help rebuild Iraq after a war that many nations opposed.
Diplomats at the United Nations in New York yesterday suggested that Security Council resolutions on providing humanitarian aid to Iraq would fare better if presented by Secretary-General Kofi Annan instead of by two of the war's main participants - the United States and Britain.
Annan was hardly neutral on the war, lamenting that "war has come to Iraq for the third time in a quarter of a century."
But Annan and members of the Security Council - deeply split after failing to agree on a resolution condoning the war - seemed prepared to unify on resolutions paving the way for post-war aid.
Even though Germany continued to condemn the war - with Foreign Minister Joschka Fischer calling it "the worst of all solutions" - the German government indicated that it would join Europe and the world in reconstruction.
Also yesterday, leaders of the European Union convened in Brussels for a scheduled meeting expected to be dominated by Iraq as the group struggled to repair the rift created during the buildup to war.
Pointing out the profound splits, Greek Prime Minister Costas Simitis vowed that his nation, which holds the EU's rotating presidency, "will do all it can so that we come to a common position to enable Europe to play a role at the next stage."
British Foreign Secretary Jack Straw pledged about $125 million in humanitarian aid for Iraq. He said Britain "will be arguing for the European community to come together and recognize we have a common agenda" working for Iraq reconstruction.
Despite angry exchanges in recent days between Straw and his French counterpart, Foreign Minister Dominique de Villepin, Straw insisted that "personal relations are I think very good. ... I think we will get through this period."