Mr Bercow's extraordinary attack reignited controversy over the invitation to Mr Trump, provoking applause from MPs who oppose the US president, and drawing accusations the Speaker was "insulting" the UK's closest ally.
The Speaker appeared to brand Mr Trump a "racist" as he said the president's travel ban on Muslims from seven countries, and refugees, had hardened his hostility to any high profile Westminster address during the visit.
"I feel very strongly that our opposition to racism and to sexism and our support for equality before the law and an independent judiciary are hugely important considerations in the House of Commons," Mr Bercow told MPs as he said he would not wish to invite Mr Trump to address them.
The Speaker said he was "strongly opposed" to the idea of an address to both houses of parliament by Mr Trump before the travel ban, and was now "even more strongly" against such a invitation.
Republican congressman Joe Wilson criticised the Speaker's comments, telling BBC Newsnight: "That's very disappointing, because if ever in recent years there's been a more pro-British president of the United States, it's Donald Trump."
"It's been by his words, his assurances with Prime Minister May of 100% of standing with Nato, and working to create trade relationships.
"But, it's also been symbolic. He was the one who returned Winston Churchill - the bust - to the Oval Office.
"I consider it too, sadly, a slap at the Republican Party. It was the leaders of our party that actually placed the bust of Winston Churchill in the US Capitol Building and we urge all persons to come visit our Capitol Building."
Downing Street moved to reaffirm its backing for the visit, after the Speaker's fierce intervention, stating: "We look forward to welcoming the president to the UK later this year. The dates and arrangements for the state visit will be worked out in due course."
Number 10 has insisted it is too early in the process to say if Mr Trump would be offered the honour of addressing MPs and peers in Westminster.
Former Ukip leader Nigel Farage said the Speaker had "insulted" Mr Trump.
"I think the speaker of the House of Commons should be neutral. To have expressed political opinions in the way he did today devalues his great office, is insulting to President Trump," he told the BBC.
The row erupted after Mr Bercow said addressing Parliament was "not an automatic right, it is an earned honour" for foreign leaders.
Labour leader Jeremy Corbyn backed the Speaker, tweeting: "Well said John Bercow. We must stand up for our country's values. Trump's state visit should not go ahead."
The Lord Speaker, Tory former Cabinet minister Lord Fowler, was not consulted by Mr Bercow and will make his own statement on the issue to peers on Tuesday.
Chairman of the Commons Foreign Affairs Committee Crispin Blunt said: "He has no idea whether he will be speaking for a majority of the House of Commons, and this is why Speakers do not express their opinion.
"That's the entire point, otherwise they can't remain neutral and above the political fray."
Iraqi-born Tory MP Nadhim Zahawi, who sharply criticised Mr Trump's travel ban after learning he could be caught up in it, suggested Mr Bercow was a hypocrite.
Mr Zahawi said the Speaker had invited Chinese president Xi Jinping despite MPs being unhappy about his policy on Tibet, and the emir of Kuwait, which bans British dual nationals of Israeli origin, to speak in Parliament.
Mr Bercow should now "think about" his position and explain his remarks to Parliament, Mr Zahawi said.
He told BBC Radio 4's Today programme: "I think it is, in my book, unwise and he opens himself up to the accusation of hypocrisy, that's my point.
"I just think it's unwise on the Queen's Sapphire Jubilee to take a political position so blatantly against the elected leader of our closest ally when we are urging them, as I was last week - I am against the travel ban, especially for banning refugees from Syria who are desperate, who have been vetted - but it's unwise to ban the legitimately elected president of the United States of America, our closest ally when we're trying to urge them not to shoot from the hip, not to ban people, to exercise restraint, look at evidence.
"Yet we are now, or at least the Speaker of Parliament, who has a big, big responsibility, is now sort of talking the language of bans."
Mr Zahawi said he wanted Mr Trump to come to Parliament so he could "eyeball him" and make his feelings clear about the travel ban.
Communities Secretary Sajid Javid was asked if the Speaker had overstepped the mark, and he told BBC Breakfast: "Anyone who knows the Speaker knows that he's perfectly capable of speaking his own mind."
Pressed on whether the Speaker is supposed to remain neutral, Mr Javid said: "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, and it's very clear that this is the choice of the American people, and it's manifestly in our self interest as a country to get on with that person and that's why President Trump is very welcome in the United Kingdom."
Mr Javid said the US is the country's "most important ally", and asked if he thinks Mr Trump should be allowed to address Parliament, he said: "I think he should be welcome in this country.
"The decision about Parliament is a decision for the Speaker and the Lord Speaker.
"That's something that Government can't get involved in, but it's very clear that we should be working with the US president and that he should be absolutely welcome to our country."
It was put to the Communities Secretary he had retweeted a statement in December 2015 which said anyone who backed Mr Trump was "certified insane" and he was asked if he wanted to retract it.
He replied: "That's not something I've ever said. And what matters is that whoever is sitting in that office, it doesn't matter who it is, that is a person that we need to get on with, and we should reach out with and we should work with."
Mr Javid told the programme: "It is absolutely in our self interests as a country that we work with the United States.
"It's our most important ally, and whether that's the president, its legislators, its governors, we should be reaching out across the board and working with our allies."