(Adds comment from British opposition leader)
By Kylie MacLellan
BELEK, Turkey, Nov 16 (Reuters) - Prime Minister David Cameron said on Monday he wanted Britain to carry out air strikes against Islamic State militants (ISIL) in Syria but still needed to convince more lawmakers to back such action.
"I have always said I think that it is sensible that we should: ISIL don't recognize a border between Iraq and Syria and neither should we but I need to build the argument, I need to take it to parliament, I need to convince more people," Cameron told BBC radio.
"We won't hold that vote unless we can see that parliament would endorse action because to fail on this would be damaging. It is not a question of damaging the government it is a question of not damaging our country and its reputation in the world."
Britain is involved in bombing in Iraq but Cameron lost a parliamentary vote in 2013 on plans to bomb Syrian President Bashar al-Assad's forces.
To avoid a similar embarrassing defeat on extending British airstrikes against Islamic State to Syria, Cameron is seeking the backing of the opposition Labour Party before bringing the issue to a vote.
Although some Labour lawmakers have expressed support, their leader Jeremy Corbyn is opposed to further air strikes and said on Monday he was not planning to allow his party members to vote with their conscience in a so-called "free vote".
"I am just not convinced that a bombing campaign will actually solve anything - it may well make the situation far worse," he said. "We will come to a position as a party on this... I don't think a free vote is something that we're offering."
Critics say a broader peace plan rather than more bombing is needed. Cameron said on Monday he agreed airstrikes would not be enough.
"People want to know there is a whole plan for the future of Syria and the future of the region because it is perfectly right to say that a few extra bombs and missiles won't transform the situation," he told a news conference at a Group of 20 (G20) summit in Turkey.
"The faster we can degrade and destroy ISIL the safer we will be, but we will only be safe in the longer term if we can replace that ungoverned space ... with a proper Syrian government."
However, Cameron said he would take immediate direct action if British interests were at stake, citing drone attacks which had killed British militants in August. (Additional reporting by William James in London, writing by Michael Holden and Kate Holton, editing by Stephen Addison)