(Corrects wording of paragraph 2)
* Cabinet agrees on need to act to deter chemical attacks
* Trump says decisions on Syria to come "fairly soon"
* Corbyn urges U.N. involvement in investigation
By David Milliken and Alistair Smout
LONDON, April 13 (Reuters) - British Prime Minister Theresa May won backing from her senior ministers to take unspecified action with the United States and France to deter further use of chemical weapons by Syria after a suspected poison gas attack on civilians.
The prospect of a confrontation between Russia, the Syrian government's ally, and the West has loomed since Trump said on Wednesday that missiles "will be coming" in response to the attack in the Syrian town of Douma on April 7.
Trump has since tempered those remarks and the White House said no final decisions on possible actions had been taken.
Russia has warned the West against attacking its Syrian ally President Bashar al-Assad, who is also supported by Iran, and says there is no evidence of a chemical attack in Douma, a town near Damascus which had been rebel-held until this month.
May has said "all indications" point to Syrian responsibility for the attack. She told her senior ministers on Thursday the Douma events showed a "deeply concerning" erosion of international legal norms barring the use of chemical weapons.
"Cabinet agreed on the need to take action to alleviate humanitarian distress and to deter the further use of chemical weapons by the Assad regime," a spokeswoman for the prime minister said in a statement after the meeting.
Ministers agreed that May should continue to work with the United States and France to come up with the right response. The statement made no specific reference to military action.
Later, May's office said she had spoken with Trump by telephone, and the two had agreed it was vital to challenge Assad's use of chemical weapons, and that they would continue to work closely together to do so.
Opposition Labour Party leader Jeremy Corbyn, a veteran anti-war campaigner, said Britain should press for a U.N.-led investigation rather than follow the lead of the United States.
May has said that Russia's veto at the Security Council of a vote to create a new inquiry on chemical attacks meant the U.N. could have no role in investigations.
"The government appears to be waiting for instructions from President Donald Trump on how to proceed," Corbyn said in a statement.
"Britain should press for an independent U.N.-led investigation of last weekend's horrific chemical weapons attack so that those responsible can be held to account."