In the UK an online petition titled "Prevent Donald Trump from making a State Visit to the United Kingdom" has gained over 900,000 signatures in less than 24 hours making it eligible for a parliamentary debate.
Any petition with more than 100,000 signatures must be considered for a debate in Parliament, though not a binding vote.
However, Downing Street confirmed that Theresa May would not be withdrawing her invitation to Trump because it remained "substantially in the national interest".
The British government has reportedly rejected a petition to prohibit US President Donald Trump from being invited on an official visit.
The petition also precludes President Trump from meeting with The Prince of Wales in any official capacity: "Donald Trump's well documented misogyny and vulgarity disqualifies him from being received by Her Majesty the Queen or the Prince of Wales".
But criticism of May's wooing of Trump erupted when - only hours after the prime minister had left the White House - the president signed an executive order suspending all travel to the US of citizens of Iran, Iraq, Sudan, Somalia, Syria, Yemen and Libya for 90 days.
After he first floated the idea of banning Muslims from America a year ago, a similar petition signed by half a million people asked he be barred from entry to the UK.
News spread over the weekend of Trump's travel ban, and by 10 am on Monday, the number of signatures on the petition had soared, and it's still rising fast.
Buckingham Palace has declined to comment.
There's growing anger at his executive order clamping down on immigration to the United States and the petition says he shouldn't be allowed to meet the queen. During both visits, May had refused to condemn Trump's executive order.
Thousands of people are expected to protest against the ban outside Downing Street tonight.
Meanwhile, a march to the United Kingdom premier's Downing Street residence is expected to attract thousands of Londoners on Monday, after more than 16,000 people said they would attend it in an online campaign.