The Remain-backing Labour Party MP said there was a “risk” of Britain looking “isolated and desperate” in the wake of its European divorce.
He insisted Speaker Bercow wanted to send a “clear message” to Theresa May, warning her not to sacrifice British “values” for the sake of striking an agreement.
Addressing MPs on Monday, Speaker Bercow said: “An address by a foreign leader to both houses of parliament is not an automatic right, it is an earned honour.
“Before the imposition of the migrant ban I would, myself, of being strongly opposed to an address by President Trump in Westminster Hall.
Stephen Kinnock claimed John Bercow's Trump rant contained a Brexit message
We have here is a real risk of the United Kingdom looking both isolated and desperate
“After the imposition of the migrant ban by President Trump I am even more strongly opposed to an address by President Trump in Westminster Hall.”
He concluded that he would use his powers as one of three official “key holders” for events in Westminster to attempt to block a visit.
“I think what John Bercow did yesterday was send a very clear message to our Government, which was that just what has happened because of Brexit it doesn’t mean we are now going to be curtailing around the world sacrificing the values we have cherished and held dear for decades because we are desperate.
“So, I think it was actually a very smart, diplomatic move to set out our values as a country and say we recognise the risk of looking increasingly isolated.
“Let’s not allow that to push us into hasty ill-advised decisions…”
But Mr Kinnock’s comments were rebuked by Conservative MP John Whittingdale, who accused his parliamentary colleague of warping Speaker Bercow’s speech into a “political statement”.
He added that it was wrong that the Speaker as seen to be “siding” with the opposition, rather than the Government.
“The Speaker was cheered by SNP members, Labour members and heard in silence by on the Government benches,” Mr Whittingdale said.
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President Trump signed an executive order banning immigration to the USA from seven 'muslim' countries. This led to protests across America and, now, the UK.
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Britons protest against US President Trump's executive order on immigration
“That is not a good thing when the Speaker is seen to be so clearly siding with one side of the House rather than the other.”
However, Government minister Sajid Javid refused to be drawn into a debate on whether Speaker Bercow should relinquish his role after the controversy.
The Communities Secretary having been asked if the Speaker had overstepped the market, he responded: “Anyone who knows the Speaker knows that he’s perfectly capable of speaking his own mind.”
He added: “What’s important is that we have full respect for the office of the President of the United States and whoever sits in that office at any time.”
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