Story highlights British government reserves the right to ban Trump after petition surpasses 500,000 signatures

UK Prime Minister David Cameron had previously called the billionaire "stupid" and warned against a visit

(CNN) The United Kingdom isn't formally barring Donald Trump from entering its borders -- at least not yet.

The British government on Wednesday offered a pointedly inconclusive response to an online citizens' petition asking that Trump be banned from the country.

In its statement, the government reaffirmed the power of Home Secretary Theresa May to "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," but does not clearly state whether her office would apply that criteria to Trump.

"The Home Secretary has said that coming to the UK is a privilege and not a right," the official comment reads. "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."

It goes on to recall comments made by PM David Cameron, who, in speaking to Parliament after Trump launched his proposal to halt the immigration of Muslims into the U.S., called the billionaire "stupid" and "three times a loser."

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