"Before the imposition of the migrant ban I would myself have been strongly opposed to an address by President Trump in Westminster Hall," said Mr Bercow, one of three officials who would have to approve the move.
"After the imposition of the migrant ban by President Trump I am even more strongly opposed."
Prime Minister Theresa May has come under intense pressure for the invitation for Mr Trump to make a state visit, which she extended while at the White House just hours before he announced his travel ban.
More than 1.8 million people have signed a public petition calling on ministers to cancel the visit, which MPs are due to debate, later this month.
Mr Bercow said that decision was above his pay grade.
"However, as far as this place is concerned, 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," he said.
But a speech to both Houses of Commons and Lords has been a feature of many previous state visits, including one by Barack Obama in 2011.
Some 163 MPs have signed a parliamentary motion opposing an address by Mr Trump, citing the travel ban and his comments on torture and women.
Mr Bercow's statement sparked cheers and clapping from the opposition benches.
Earlier, Ms May told MPs that at a summit last week, she had urged her fellow European leaders to "engage patiently and constructively" with the new US administration.
Mr Trump's criticism of the NATO military alliance and his prediction that the EU could fall apart following Britain's vote to leave has caused alarm in European capitals.