The announcement by the Yarmouk Martyrs' Brigade was posted on the Facebook page that was used to disclose the detention Wednesday, The Washington Post reported.
The organization also called on the United Nation to send a convoy to get the observers.
A U.N. statement said the peacekeepers were on a regular supply mission in the Golan Heights, a demilitarized zone between Israel and Syria, when they were detained by about 30 armed fighters. A U.N. official said the peacekeepers were from the Philippines.
A video that accompanied Wednesday's post in which the kidnappers said the observers would not be released until Syrian President Bashar Assad withdrew troops from the area was deleted, the Post said.
"With God's help we managed to secure a group of U.N. members working in the border town of Jamleh after they were victims of the criminal shelling of Assad's gangs," the statement posted Thursday said. "We request from the United Nations to send us a security convoy so that we can deliver them to the organization."
Najib Ghadbian, the Syrian National Coalition's ambassador to the United States and the United Nations, called the incident a "preventative security measure," not a kidnapping.
In New York, the U.N. Security Council, in a statement, blamed "armed elements" of the Syrian opposition for the abduction and demanded the "unconditional and immediate release" of the observers.
Israel said it would not intervene in the matter, expressing confidence that the United Nations could secure release of its peacekeepers, the British newspaper The Guardian reported.
Vitaly Churkin, Russia's U.N. ambassador, said, "It seems that lately some people are trying very hard in order to extend the geography of the Syrian conflict. ... Somebody is trying very hard in order to blow this crisis up."
The incident came as the United Nations said the millionth refugee fled from Syria and the nearly two years of violence, the Post said. The huge majority of the refugees have fled to Lebanon, Jordan, Turkey and Iraq.
Earlier Wednesday, Britain announced it secured an exemption to a European arms embargo against Syria, allowing it to supply non-lethal military equipment to the Syrian Opposition Coalition, the umbrella political movement, the Post reported. British Foreign Secretary William Hague said the supplies would include body armor and armored four-wheel-drive vehicles to help the rebellion's civilian leaders to protect themselves.
The $20 million package follows the U.S. offer of $60 million in non-lethal aid made last week.
The international humanitarian group Doctors without Borders said in a report issued Wednesday, the conflict is taking a toll on the country's health sector.
"Health workers and medical facilities are still receiving threats and medical structures are targeted and destroyed," the report said.
Syria's health care system once functioned to a high standard, the report said, but since the crisis, health facilities have been targeted, injured people arrested and physicians hunted, forcing development of a clandestine healthcare network.
"According to the Syrian authorities, 57 percent of public hospitals in the country have been damaged and 36 percent are no longer functional," the report said. "For a complete picture of the devastation, though, makeshift hospitals set up by the opposition and subsequently destroyed by the army should also be added to the tally."
The report said major obstacles prevent more aid reaching government- and rebel-held areas.
"The government is limiting humanitarian aid, keeping tight control on any aid that flows through Damascus and refusing to allow aid organizations to cross the front lines from the capital," the report said. "Meanwhile, in the north of the country, insecurity caused by fighting and bombing is being compounded by political and diplomatic constraints that seriously impact the amount of aid that can be delivered."
The Arab League said its members may now arm rebels fighting the Assad regime while offering a rebel coalition the league seat Damascus once occupied.
League ministers meeting in Cairo "stressed the right of each state according to its wishes to offer all types of self-defense, including military, to support the resilience of the Syrian people and the Free [Syrian] Army," the 22-country bloc said in a statement.
The league earlier supported only humanitarian aid and diplomacy.
League Secretary-General Nabil al-Araby said Wednesday the Syrian National Coalition, an opposition umbrella group backed by the West and Arab states, was invited to attend the league summit in Doah, Qatar, March 26-27.
SNC would retain Syria's seat in the organization "until elections [lead] to the formation of a government to assume the responsibilities of power in Syria," the league said.
The league suspended Syria's membership in November 2011.
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