"The government has a policy of not routinely commenting on individual immigration or exclusion cases," a statement said.
"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.
"The Home Secretary has said that coming to the UK is a privilege and not a right and she will continue to use the powers available to prevent from entering the UK those who seek to harm our society and who do not share our basic values. Exclusion powers are very serious and are not used lightly. The Home Secretary will use these powers when justified and based on all available evidence.
"The Prime Minister has made clear that he completely disagrees with Donald Trump’s remarks. The Home Secretary has said that Donald Trump’s remarks in relation to Muslims are divisive, unhelpful and wrong."
"The Government recognizes 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 marginalization amongst those we endeavor to protect."
Donald Trump had called for a "total and complete shutdown" of Muslims entering the United States until "our country's representatives can figure out what is going on."
"Mr. Trump stated, Without looking at the various polling data, it is obvious to anybody the hatred is beyond comprehension. Where this hatred comes from and why we will have to determine. Until we are able to determine and understand this problem and the dangerous threat it poses, our country cannot be the victims of horrendous attacks by people that believe only in Jihad, and have no sense of reason or respect for human life," the statement read.
The petition -- "Block Donald J Trump from UK entry" -- was started by someone using the name Suzanne Kelly and, in the United Kingdom, the government is obliged to respond to such appeals that receive over 10,000 signatures. If petitions reach 100,000 signatures, they are considered for debate in Parliament.