Calls for Parliament to return early from its summer break have been backed by Commons Leader Jack Straw's aide.
A recall decision would be a matter for the Speaker Michael Martin
Labour MP Paddy Tipping, Mr Straw's parliamentary private secretary, said there was a strong case for a recall so ministers could hear people's views.
The terror alert prompted Labour MP Mohammed Sarwar to say it was imperative to reconvene the Commons.
But Tory David Davis said MPs should not "jump through hoops" every time a terrorist plot was foiled.
Up to 100 MPs - most of them Labour - are writing to Mr Straw to demand a recall of Parliament to debate the crisis in the Middle East, according to The Guardian newspaper.
Mr Tipping told The World at One on BBC Radio 4 that he had not seen or signed the letter.
But he said the government had made clear Parliament could be recalled if necessary.
"There is a strong case for Parliament to meet to discuss the matter," he said.
"It would not be unusual and it is important that different views are aired.
"There are strong feelings in the Parliamentary Labour Party about the approach the government has taken and it is important, I think, that the government has the opportunity to hear these different views and reflect them directly."
Mr Sarwar said news that the UK terror threat had been raised to "critical" as 21 people were arrested over an alleged plot to attack passenger planes would increase pressure for a recall.
"The people in this country expect the members of Parliament, at a time of crisis, to take the lead," he said.
Labour MP Shahid Malik, another supporter of a recall, added: "Today's events may well have an impact, but I think the momentum was always there.
"We want to make sure that the representations made to us by our constituents are actually debated in the chamber of the House. I think that is the democratic thing to do."
Shadow home secretary Mr Davis said whatever the arguments for a resumption of Parliament to discuss the Middle East crisis, MPs should not return because of the terrorism arrests.
Any decision would rest with the Speaker, Michael Martin, based on the advice given by ministers.
Downing Street has refused to comment in advance of any letter being delivered.
A No 10 spokeswoman said it was "a matter for the leader of the Commons".
The organisers of the letter are reported to have been in discussion with the Liberal Democrats and the Scottish National Party.
Jon Trickett, chairman of the 50-strong Compass group of left-wing Labour MPs, is said to have been among those behind it.
He told the Guardian: "In this crisis, Parliament needs to speak for the nation.
"We are living in a 24/7 society, yet our Parliament seems so ossified that it goes into recess for 11 weeks and there seems no way for backbenchers to bring back MPs."