"For those of us seeking to serve the people of this country, it is our duty to drive the dialogue on how best to confront and defeat this brand of terrorism. That is what UKIP will be doing today and beyond. Therefore, I refuse to suspend campaigning because this is precisely what the extremists would want us to do," Nuttall said, as quoted in a statement published on the party website.
Earlier in the day, the Conservative Party, the Labour Party and the Scottish National Party all announced that they were suspending national campaigning following the incident in London.
According to the local authorities, at least seven people were killed and 48 more injured. UK Prime Minister Theresa May said that the incident was treated as a terrorist attack.
The general election in the United Kingdom is expected to be held on Thursday. London Mayor Sadiq Khan said earlier that the election would take place despite the attacks.