Airstrikes on Syria are set to be debated by MPs later in the wake of the Tunisia beach massacre that saw at least 29 Britons killed.
Defence Secretary Michael Fallon is expected to make a case for allowing RAF bombers to attack Islamic State targets.
But he will insist no military action will be taken without a vote in the Commons.
The Commons gave the go-ahead to bombing of militant positions in Iraq last year, but MPs were not asked to approve wider action.
The Prime Minister's official spokeswoman said: "The Prime Minister has been clear on the need for us to be crushing Isil in both Iraq and Syria.
"Clearly, Isil is seeking to find areas from which it can operate, from where it can seek to threaten people here in Britain, and as part of what the PM was talking about in terms of having a 'full spectrum' response, that clearly means not just focusing on one area where they are, but looking at a whole range of areas and how Isil are operating."
The spokeswoman said that "a lot has happened" since the chemical weapon attack by Syrian president Bashar al Assad which sparked the previous proposal for airstrikes.
She added: "Therefore the Prime Minister is clear that we absolutely should be thinking about are we doing enough, and in the right areas, to tackle Isil."