MPs would vote to reverse Government plans to axe 9,500 troops by 2025, according to Tobias Ellwood.
The former Conservative Party defence minister, who now chairs the Defence Select Committee, pressed ministers to hold a Commons vote to decide whether to halt the proposals in light of Russia's invasion of Ukraine.
The Government wants to cut the size of the regular British Army from 82,000 troops to 72,500.
Mr Ellwood told the Commons: "Can I strongly commend the Government's exemplary support for Ukraine, but when the head of the British Army compares today to 1937 we must listen and we must act.
"It's clearly not time to be cutting our Army by 10,000 troops because this sends a clear message to (Russian President Vladimir) Putin that we're not in it for the long haul, we can't sustain two battlegroups in Estonia and place pressure on the Army to conduct all its other duties to keep the nation safe.
"Can we have a debate and indeed a vote on reversing these cuts?
"If there was a free vote I know how the House would act and they'd have the nation's support."
In reply to Mr Ellwood, Leader of the House of Commons Mark Spencer said: "He will be aware that we're increasing defence spending by over £24bn over the next four years, we've announced another £1bn in military support to Ukraine – taking our total military support to £2.3bn. That is more than any other country other than the United States.
"We have a huge, proud record of our military around the world and in the UK, and we will continue to support them."