John Bercow, who is known as an outspoken Speaker, said it was not an "automatic right" but an "earned honour" for world leaders to address both Houses of British Parliament from Westminster Hall.
"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. I would not wish to issue an invitation to President Trump," said Bercow, who is one of three traditional "key holders" to the Westminster Hall.
The unusually strong statement from a Speaker, who is expected to remain politically neutral, triggered much opposition from ruling Conservative party members.
"Anyone who knows the Speaker will know that he speaks his mind. But he doesn't speak for the government," said UK communities minister Sajid Javid.
"The government is very clear: President Trump is the leader of our most important ally, he's elected fairly and squarely, and it's manifestly in our national interests that we reach out to him and we work with him, and he visits us in the UK," he added, reflecting the official government stance.
A petition opposing such an honour for him in the wake of his executive order against nationals of seven Muslim majority countries attracted over 1.5 million signatures and is set to be debated in the Commons on February 20.
Addressing both houses of Parliament is often, but not always, part of the many rituals involved in a state visit.
Barack Obama was the last US President who was invited for such an honour in 2012.
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