Shadow Scottish Secretary Ian Murray opposes Syrian air strikes
The shadow Scottish secretary has said he will oppose air strikes against the so-called Islamic State group in Syria in a vote in the Commons.
The SNP urged Mr Cameron to publish his draft motion on air strikes as early as possible to allow proper scrutiny.
Both Labour and the SNP had called for a two-day debate in the House of Commons.
Prime Minister David Cameron wants MPs to vote in favour of the RAF being allowed to target Islamic State militants in Syria as well as Iraq.
But with the SNP and several of his own backbenchers opposed, the prime minister will need the support of many Labour MPs if he is to win any vote.
Ahead of attending a shadow cabinet meeting with Mr Corbyn on Monday morning, shadow Scottish Secretary Mr Murray, told BBC Radio Scotland he would vote against air strikes as he did not think they would improve the situation in Syria.
Responding to Mr Corbyn agreeing to give Labour MPs a free vote, Scottish First Minister and SNP leader Nicola Sturgeon tweeted: "So a party that says it is anti-airstrikes has just made a vote for airstrikes more likely?! Go figure."
Ms Sturgeon's predecessor, Alex Salmond, who is the SNP's foreign affairs spokesman, told the BBC his party's position remained "very clear" in that the SNP was "listening to what the government is saying but we are not persuaded and as things stand we will be voting against the extension of military action into Syria".
He also criticised Mr Corbyn for allowing Labour MPs a free vote, describing his actions as an error of judgment and an ''abdication of responsibility''.
Mr Cameron had said he would not hold a vote until he was convinced he could win the backing of MPs to carry out air strikes in Syria as well as Iraq.
The SNP has now called for the prime minister to publish his government's draft motion on air strikes as early as possible to "allow appropriate scrutiny".
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Labour is deeply divided over the issue of air strikes.
It had been reported that some members of the shadow cabinet were prepared to resign if they were ordered to vote against them, and that about 100 Labour MPs were in favour of air strikes.
Mr Murray said: "He [Mr Corbyn] may try and impose this on the shadow cabinet. I think that would be wrong in this particular instance because I think people have very strong views one way or another."
Mr Cameron set out his case for Syrian air strikes last week, when he told MPs there were 70,000 "moderate" Free Syrian Army (FSA) and Kurdish fighters on the ground who would be able to take and hold territory.
But Mr Murray said he believed the prime minister's case fell down on three grounds: a lack of capacity in the Free Syrian Army; uncertainty over the position of Russia and what to do with Syrian president Bashar al-Assad; and the opposition to air strikes from the people of Raqqa, the Syrian city where Islamic State has its headquarters.
He said: "If there is a vote held this week I would vote against.
"The prime minister has got a lot of work to do and I just don't think the case has been made that this will make any difference at all to the position in Syria."
Mr Murray said Scottish Labour leader Kezia Dugdale was also opposed to air strikes, but added: "There are wide views on this particular issue - it is an incredibly emotive issue."
The Campaign for Socialism, a left grouping within Scottish Labour, had urged Mr Corbyn to call a whipped vote "to ensure that David Cameron cannot win a vote to launch UK airstrikes".
MPs rejected a vote for air strikes against Syrian government targets in 2013. However, it is taking part in air strikes against IS in Iraq after MPs backed the move last year.