The Department of Homeland Security and the Trump administration did not respond to requests for comment on Friday evening on the possibility of a privately funded effort to build the wall.

Typically, GoFundMe campaigns can still collect money even if they do not meet their goal.

But Bobby Whithorne, a spokesman for GoFundMe, said in a statement on Friday that Mr. Kolfage’s original campaign page had said “If we don’t reach our goal or come significantly close we will refund every single penny” and that “100% of your donations will go to the Trump Wall. If for ANY reason we don’t reach our goal we will refund your donation.”

Mr. Whithorne said that since the campaign was not going to reach the $1 billion goal, and that both GoFundMe and Mr. Kolfage had determined the money raised could not be given to the federal government, GoFundMe had contacted all donors to the original campaign about the refund.

Donors can ask for a refund immediately, Mr. Whithorne said, but if they do not choose to redirect their money to the nonprofit, they will automatically receive a refund in 90 days.

Immigration advocacy groups had condemned the GoFundMe campaign as a xenophobic result of fearmongering about immigrants. Some had started competing fund-raising campaigns to raise money for Refugee and Immigrant Center for Education and Legal Services, a Texas nonprofit known as Raices.

Jonathan Ryan, president and chief executive of Raices, said that despite the change in Mr. Kolfage’s campaign, the original critiques of it still stand.

“It’s a difference without a change,” Mr. Ryan said. “The wall remains the wrong direction for us as a country, something that will not help advance any of our national interests and that would only serve to further harm vulnerable refugees and immigrants seeking protection in our country.”