More than 500,000 people have signed the parliamentary e-petition.
In response, the government said it recognised the strength of feeling against Mr Trump's comments, which are expected to be debated by MPs.
Ministers previously criticised his remarks but disagreed with banning him.
Any petition with more than 10,000 signatures on the parliament website gets a government response, and if one gets more than 100,000 signatures it is automatically considered for debate in Parliament.
The cross-party Commons petitions committee is due to meet next week to decide whether to hold a parliamentary debate on the petition to ban Mr Trump.
Given the number of signatures, there is a presumption it will be debated.
In its response, the government said it did not comment on individual immigration and exclusion decisions.
"The home secretary may exclude a non-European Economic Area national from the UK if she considers their presence in the UK to be non-conducive to the public good," it said, adding that Theresa May had said coming to the UK was "a privilege and not a right".
"Exclusion powers are very serious and are not used lightly" and would only be used "based on all available evidence", it said, adding: "The government recognises the strength of feeling against the remarks and will continue to speak out against comments which have the potential to divide our communities, regardless of who makes them.
"We reject any attempts to create division and marginalisation amongst those we endeavour to protect."
Prime Minister David Cameron has labelled Mr Trump's comments "stupid" but said he did not support a ban, telling MPs the tycoon would "unite us all against him" if he visited the UK.
The government has responded to a petition calling for presidential hopeful Donald Trump to be banned from the UK after he proposed a temporary halt on Muslims entering the US.