* Government, rebels accuse each other of chemical attack
* U.N. won't focus on second alleged attack in Damascus
* West urges U.N. to probe all chemical attack reports
* U.S. official: Evidence suggests no chemical weapon used (Adds U.S. official doubting use of chemical weapons)
By Michelle Nichols and Louis Charbonneau
UNITED NATIONS, March 21 (Reuters) - The United Nations said on Thursday it would investigate Syria's allegations that rebel forces used chemical weapons in an attack near Aleppo, but Western countries sought a probe of all claims concerning the use of such banned arms.
"I have decided to conduct a United Nations investigation into the possible use of chemical weapons in Syria," said Secretary-General Ban Ki-moon. The investigation will focus on "the specific incident brought to my attention by the Syrian government," he told reporters.
Syria asked Ban to investigate an alleged chemical weapons attack by "terrorist groups" near the northern city of Aleppo on Tuesday, said Syrian U.N. Ambassador Bashar Ja'afari.
The deaths of 26 people in that rocket attack became the focus of competing claims on Wednesday from Syrian President Bashar al-Assad's supporters and opponents, who accuse each other of firing a missile laden with chemicals.
The Syrian opposition reported a second chemical weapons attack on Tuesday near Damascus.
Ban made clear the focus of the investigation he announced would be on the Aleppo attack.
"I am of course aware that there are other allegations of similar cases involving the reported use of chemical weapons," he said, adding the United Nations would be cooperating with the Organization for the Prohibition of Chemical Weapons and the World Health Organization.
"My announcement should serve as an unequivocal reminder that the use of chemical weapons is a crime against humanity," Ban said.
U.S. Ambassador to the United Nations Susan Rice said Washington wanted any serious allegations regarding the use of chemical weapons in Syria to be investigated.
"The United States supports an investigation that pursues any and all credible allegations of the possible use of chemical weapons in Syria, and underscores the importance of launching this investigation as swiftly as possible," Rice said in a statement.
France and Britain wrote to Ban on Thursday to draw his attention to the second alleged attack near Damascus, as well as one in Homs in late December. The rebels blame Syria's government for all three incidents
"Given the gravity of these allegations we judge it essential that all the pertinent facts concerning these allegations are swiftly investigated," France and Britain wrote. "We therefore request that you launch an urgent investigation into all allegations as expeditiously as possible."
U.S. and European officials say there is no evidence of a chemical weapons attack. If one is confirmed, it would be the first use of such weapons in the two-year Syrian conflict, which the United Nations says has killed 70,000 people.
A U.S. official went so far as to say that it increasingly appeared a chemical weapon was not used in Syria this week, although U.S. intelligence agencies have not yet reached a final conclusion.
U.N. spokesman Martin Nesirky said Ban was reviewing the British and French request. It was not immediately clear whether the Syrian government's permission would be required to broaden the investigation to include all three alleged attacks. One U.N. diplomat said Assad's government would have to consent to it.
Russian Ambassador Vitaly Churkin said on Wednesday the British and French demand for an investigation into other attacks was an attempt to delay the U.N. probe of the Aleppo incident. He praised Ban's decision to begin an investigation.
The dispute over the scope of the U.N. investigation highlights the chasm between Russia's position toward the Syrian government, its ally, and that of the Western powers that support the opposition trying to oust Assad. The deadlock on the council has left it powerless to act on Syria.
Syria is not a party to the Chemical Weapons Convention, an international treaty that bans chemical weapons. For months, the United States, Israel and European countries have voiced concerns about the security of Syria's chemical arms stockpile.
Israel, Myanmar, Angola, Egypt, North Korea, Somalia and South Sudan are the only other states that have not joined the 1997 convention.
This is the first time the Organization for the Prohibition of Chemical Weapons, which oversees the convention, has been asked to investigate in a conflict zone. A team of inspectors is ready to travel to Syria when it is safe to do so.
The World Health Organization said it would support the investigation as requested by Ban. "The overall mandate, mission composition and operational conditions, including safety and security, have yet to be finalized. No start date has been set," said WHO spokesman Gregory Hartl.
Ban urged the Syrian government and rebels to cooperate.
"There is much work to do and this will not happen overnight, it is obviously a difficult mission," Ban said, adding the probe would begin as soon as possible. (Additional reporting by Anthony Deutsch in Amsterdam, Stephanie Ulmer-Nebehay in Geneva, and Tabassum Zakaria and Phil Stewart in Washington; Editing by Doina Chiacu and Peter Cooney)