Last month the incumbent James Bond welcomed his first child with wife Rachel Weisz, a baby girl,
The family are based in New York City and Craig was spotted out and about with his daughter in the East Village a couple of days ago.
Wearing sports kit, a baseball cap and glasses to keep inconspicuous, the 50-year-old had his little girl strapped on in a papoose.
However, Good Morning Britain’s Morgan decided to comment on this negatively.
Yesterday morning he tweeted: “Oh 007… not you as well?!!! #papoose #emasculatedBond.”
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But apart from a series of proud dads sharing photos of themselves using the child-carrying bag, a number of celebrities have spoken out against Morgan.
This includes Captain America star Chris Evans who tweeted back: “You really have to be so uncertain of your own masculinity to concern yourself with how another man carries his child.
“Any man who wastes time quantifying masculinity is terrified on the inside.”
Morgan has since been hit by a Twitter storm which he labelled “Papoose-gate.”
The TV presenter has even put himself forward as the next Bond with a picture of himself in a dinner jacket.
He tweeted: “One thing’s clear after tonight’s ferocious Papoose-gate debate: we need a new James Bond.
“A 007 who looks sharp in a tux & wouldn’t be seen dead in a papoose…”