The three-judge panel said there was insufficient evidence to support charges of genocide in a war in which up to 300,000 people have died and 2.7 million have fled their homes.
Al-Bashir's government denounced the warrant as part of a Western conspiracy aimed at destabilizing the vast oil-rich nation south of Egypt.
African and Arab nations fear the warrant will destabilize the whole region, bring even more conflict in Darfur and threaten the fragile peace deal that ended decades of civil war between northern and southern Sudan. China, which buys two-thirds of Sudan's oil, supports the African and Arab positions.
Some African nations reportedly threatened to pull out of the court in retaliation for a warrant. Thirty African countries are among the court's 108 member states.
In a show of defiance Tuesday in anticipation of the decision, al-Bashir told supporters at a rally, "We are telling them to immerse it in water and drink it," a common Arabic insult meant to show extreme disrespect.
Hundreds of Sudanese waving pictures of the president and denouncing the court quickly turned out in a rally at the Cabinet building in Khartoum. Security was increased around many embassies, and some diplomats and aid workers stayed home amid fears of retaliation against Westerners.
"He is suspected of being criminally responsible ... for intentionally directing attacks against an important part of the civilian population of Darfur, Sudan, murdering, exterminating, raping, torturing and forcibly transferring large numbers of civilians, and pillaging their property," court spokeswoman Laurence Blairon said. If al-Bashir is brought to trial and prosecuted, he faces a maximum sentence of life imprisonment.
The U.N., which has a joint peacekeeping mission in Darfur with the African Union, will continue to deal with al-Bashir, U.N. spokeswoman Michele Montas said at U.N. headquarters in New York.
"President al-Bashir is the head of state of Sudan, and United Nations officials will continue to deal with president al-Bashir when they need to do so," Montas said.
Blairon rejected accusations that the warrant was part of a political plot and said the decision was made purely on legal grounds.
Al-Bashir denies the war crimes accusations and refuses to deal with the court, and there is currently no international mechanism to arrest him. The main tool the court has is diplomatic pressure for countries to hand over suspects.
The United States is not a member of the international court, but in Washington, the State Department called on all parties to the Darfur conflict to exercise restraint and cooperate with the decision, which it said could be helpful in ending the violence.
"The United States is strongly committed to the pursuit of peace in Sudan and believes those who have committed atrocities should be held accountable for their crimes," spokesman Gordon Duguid said, adding "it is evident that the government of Sudan has the brunt of the responsibility for what has happened in Darfur."
Prosecutor Luis Moreno Ocampo suggested al-Bashir could be arrested if he flies out of Sudan.
"As soon as Mr. al-Bashir travels in international airspace, his plane could be intercepted and he could be arrested. That is what I expect," the prosecutor said.
"Like Slobodan Milosevic or Charles Taylor, Omar al-Bashir's destiny is to face justice," Moreno Ocampo said referring to the former presidents of Yugoslavia and Liberia who were indicted while in office and ended up on trial in The Hague.
Sudan does not recognize its jurisdiction and refuses to arrest suspects. U.N. peacekeepers and other international agencies operating in Sudan have no mandate to implement the warrant, and Sudanese officials have warned them not to go outside their mandates.
Asked why judges, in a 2-1 split decision, did not issue the warrant for genocide, Blairon explained that genocide requires a clear intent to destroy in part or as a whole a specific group.
"In this particular case, the pretrial chamber has not been able to find there were reasonable grounds to establish a genocidal intent," she said.
She said prosecutors could ask again for genocide charges to be added to the warrant if they can produce new evidence. Prosecutor Luis Moreno Ocampo said he would study the ruling before deciding whether to keep pursuing genocide charges.
The war in Sudan's western Darfur region began in 2003, when rebel ethnic African groups, complaining of discrimination and neglect, took up arms against the Arab-dominated government in Khartoum. In 2005, the U.N. Security Council asked Moreno Ocampo to investigate crimes in Darfur.
The Rome statute that set up the International Criminal Court allows the Security Council to vote to defer or suspend for a year the investigation or prosecution of a case. It also gives the council authority to renew such a resolution.
The 52-member countries of the African Union and 26 states of the Arab League make up about a third of U.N. member states and they have said they would call for such a suspension.
But the council is sharply divided on suspending the case and is unlikely to take any action.
Some African nations reportedly have threatened to pull out of the court in retaliation for the warrant. Thirty African countries are among the court's 108 member states.
The Sudanese ruling party leadership will meet later Wednesday to decide its course of action, al-Bashir's foreign affairs adviser Mustafa Osman Ismail told state TV after the court announcement.
"This decision was not a surprise to us, but all the mechanism of the state will react. We in the Cabinet will meet tomorrow to see what steps are to be taken," Ismail said.
Rights groups welcomed the decision.
"With this arrest warrant, the International Criminal Court has made Omar al-Bashir a wanted man," said Richard Dicker, director of the International Justice Program at Human Rights Watch. "Not even presidents are guaranteed a free pass for horrific crimes. By ruling there is a case for President al-Bashir to answer for the horrors of Darfur, the warrant breaks through Khartoum's repeated denials of his responsibility."