He told the BBC he had been in talks with Labour MPs but added: "We've got to keep building the case".
He admitted it would be harder to get the support if Labour ordered its MPs to vote against air strikes in Syria.
Labour's Jeremy Corbyn, who opposes air strikes, said he had not decided whether to offer them a free vote.
MPs could vote next week on whether to extend UK air strikes against IS into Syria, but the government has said it will not call the vote unless it is certain to win.
Ministers need the support of enough Labour MPs to compensate for Conservative rebels who will vote against military intervention, and Mr Fallon said he had been briefing Labour MPs on the government's case.
It's all about the numbers. Even though the government has a majority of 12, a number of Conservative MPs - perhaps a dozen - have strong doubts about extending air strikes to Syria.
And the government will not risk a defeat in the House of Commons. In fact, it wants an emphatic win.
The government won't get the support of SNP MPs, the third largest party in Parliament, so it needs a chunk of Labour MPs with it.
Some Labour MPs had briefings with the MoD this weekend and are wrestling with the arguments, listening to constituents.
It is why Jeremy Corbyn's decision is so important.
If he allows a free vote, perhaps half his shadow cabinet and around 60 Labour MPs may vote for air strikes. If he insists on collective opposition there will be an almighty row within the Parliamentary Labour Party that could scupper the government's plans.
One shadow cabinet minster has told me there's a chance Labour will not agree a position on Monday at all and will wait for the wording of the government's motion before deciding how to vote.
It will be a crucial week.
Asked if the numbers were in place to support action, Mr Fallon said "not yet", but that ministers were "working at it"..
"You shouldn't extend military operations lightly," he said. "There are legitimate questions to answer and we're doing our best to answer them."
He also rejected suggestions attacking IS, also known as Isil, would make the UK more of a target. saying: "There are always risks in war but there is a greater risk from not doing something about Isil and leaving our streets vulnerable to the kind of slaughter we saw in Paris."
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.
Mr Corbyn, who has set out his opposition to bombing, reiterated his position, saying he "seriously questions" the government's claim there are 70,000 moderate opposition fighters on the ground.
He said: "There also has to be a recognition that if we bomb in Raqqa we are going to take out civilian lives, we may not in effect do very much damage to Isil and actually may make the situation worse not better."
The Labour leader said it would be for him to decide whether to offer a free vote to his MPs, which would mean they would not be bound to follow the party line.
He added: "No decision has been made on that yet, I am going to find out what MPs think.
"Obviously there are strong views on both directions. We will have a further discussion on this. We will make that decision not at this moment but later on."
Mr Corbyn said he had received 70,000 responses to a survey sent out to Labour supporters on Friday canvassing their opinions on air strikes, and a decision would be taken "as a party".
There is mounting pressure for a free vote, a move supported by shadow chancellor and Corbyn ally John McDonnell.
Shadow justice secretary Lord Falconer said there were "significant differences" within Mr Corbyn's top team on the issue which he did not think could be reconciled.
Former shadow business secretary Chuka Umunna said he would vote with his conscience even if ordered to follow the party line, adding on Sky News that there was "no shame in there being a broad range of views on issues of war and peace" within Labour ranks.
Both Mr Umunna and Lord Falconer said they were minded to support air strikes.
Labour MP Stephen Kinnock, who plans to oppose air strikes, said a free vote should be offered because the issue is a "matter of conscience".
But two other MPs, who both suggested they too would vote against air strikes, said they felt the vote should be whipped.
Speaking on BBC Radio 4's The World This Weekend, both Liam Byrne and Jess Phillips criticised Mr Corbyn's handling of the situation.
SNP deputy leader Stewart Hosie said his party had not been convinced by the argument for military action.
Unless the government could present a plan "to avoid the anarchy of Libya", he said, "of course we couldn't possibly support conflict in the current climate".
UKIP's Nigel Farage was dismissive of the government's strategy.
"What the prime minister and Michael Fallon were saying is, let's send another three jets, that's all we're talking about. I'm sorry, I don't believe that. I've heard these arguments over repeated military interventions."
The government does not yet have enough votes from MPs to back air strikes against Islamic State (IS) in Syria, Defence Secretary Michael Fallon said.