"I think the present status of the open border we have right now, many of us feel, does actually leave that [Paris-style terrorist attack] door open, and we need to see that resolved," Smith told the BBC.
Revising the passport-free EU-wide Schengen open border was a "critical part" of Prime Minister David Cameron’s renegotiating campaign for EU reforms, he added.
"This open border does not allow us to check and control the people that may come and may spend time. You see what happened in Paris, where they spent ages planning and plotting, so who's to say it's not beyond the wit of man that those might already be thinking about that," Smith stressed.
Key allies and members of Cameron's Cabinet have splintered off to support an "out" campaign, including London Mayor Boris Johnson and Justice Secretary Michael Gove.
After reaching the deal, Cameron argued that the United Kingdom would be "safer and stronger" within the European Union.
