Ten states, including heavyweight Saudi Arabia, "agreed to do their share in the comprehensive fight" against Islamic State of Iraq and the Levant, said a statement after a meeting between US Secretary of State John Kerry and his Arab counterparts.
With Iraq's new unity government and the Syrian opposition welcoming Obama's plan, Syrian President Bashar al-Assad's regime and powerful ally Russia strongly condemned it.
"Any action of any kind without the consent of the Syrian government would be an attack on Syria," National Reconciliation Minister Ali Haidar said.
Obama said Wednesday he had ordered the US military to expand its operations against IS, a radical Islamist group that has seized a swathe of Iraq and Syria and committed horrifying atrocities.
"Our objective is clear: we will degrade, and ultimately destroy, ISIL through a comprehensive and sustained counter-terrorism strategy," Obama said in a television address, using an alternative acronym for the group.
"I will not hesitate to take action against ISIL in Syria, as well as Iraq."
Obama announced the dispatch of another 475 military personnel to help train Iraqi forces to take on IS, bringing the total in the country to 1,600.
But he stressed that the campaign would not be a repeat of the exhausting ground wars fought by US troops in the past decade.
Instead, Washington is looking to empower partners on the ground like Iraqi and Kurdish forces, as well as Syrian rebels, to fill in territory opened up by its air power.
- Broadening the coalition -
Key to that will be improving the effectiveness of the rebels, and Obama called on Congress to swiftly authorise an operation to train and equip moderate fighters.
In Jeddah, Kerry sought crucial backing for the US campaign, meeting his counterparts from the oil-rich Gulf monarchies, as well as Lebanon, Egypt, Iraq, Jordan and NATO member Turkey.
Party to Thursday's statement, in addition to Riyadh, were Bahrain, Kuwait, Oman, Qatar and the United Arab Emirates, as well as Egypt, Iraq, Jordan and Lebanon.
"Many of the countries are already taking action against ISIL," a State Department official said.
"But the trip by the secretary is going to broaden the coalition and bring it into more focus and intensify the lines of effort."
Kerry heads to Ankara on Friday for talks there, after Turkey refused to allow its air bases to be used in the attacks on jihadists or to take part in combat operations.
Syria's opposition urged Washington to take action against Assad as well as jihadists.
The opposition National Coalition said it had "long called" for action against IS and "warned time and again of the growing threat of this extremist group".
The US announcement was praised by Baghdad, where a unity government was formed Monday to address grievances that contributed to the rise of the jihadists.
"Iraq welcomes Obama's strategy about standing with it in its war against (IS) and the terrorist groups," said Prime Minister Haidar al-Abadi's office.
But Russia said unilateral action would be a blatant violation of international law.
- Kerry 'surprised' at Russia -
"In the absence of an appropriate decision of the UN Security Council, such a step would become an act of aggression, a crude violation of the norms of international law," a foreign ministry spokesman said.
Kerry ridiculed that, saying: "I am really rather surprised that Russia would dare to assert any notion of international law after what has happened in Crimea and eastern Ukraine."
Meanwhile, British Prime Minister David Cameron said London does not rule out military action against IS in Syria, according to a spokesman, contradicting earlier remarks by Foreign Secretary Philip Hammond that Britain would not join US air strikes there.
And while saying Germany agrees IS must be challenged militarily, Foreign Minister Frank-Walter Steinmeier said his country would not participate in air strikes.
The growing IS threat was made clear after the group seized large parts of Iraq in a lightning June offensive, sweeping aside ineffective Iraqi forces.
It declared a "caliphate" in parts of Syria and Iraq it controls and has been accused of widespread atrocities, including beheadings, crucifixions, rapes and selling women into slavery.
Two captive US journalists, James Foley and Steven Sotloff, were beheaded in recent weeks, videos released by the jihadists showed.
And on Thursday, IS kidnapped 20 people in a northern Iraqi village whom they suspected of grouping to fight them, officials and witnesses said.
French President Francois Hollande will also head to Iraq on Friday for talks ahead of an international conference on Iraqi peace and security that Paris will host on Monday.
In another development, the United Nations said 45 Fijian peacekeepers kidnapped two weeks ago in the Golan Heights by Al-Qaeda-linked rebels were released Thursday and are in good condition.