"They're letting people pour into the country so they can go and vote," Trump said during a meeting with representatives of the National Border Patrol Council, the union that represents Border Patrol agents, at Trump Tower in New York.
The New York businessman provided no specifics on the accusation.
But Shawn Moran, a Border Patrol council spokesman, said after the meeting that the union was not suggesting illegal immigrants were being allowed to vote, but that U.S. immigration officials were fast-tracking applications for citizenship before the Nov. 8 election.
“They’re being ordered from above to fast-track these applications so that people are naturalized in time for the election,” he said. “We’re being told that the background checks are kind of being short-circuited and just not done as thoroughly as necessary so that these people may still qualify to be naturalized.”
Moran said Border Patrol agents were also seeing more people crossing the border with Mexico, either in hopes of gaining legal status if Clinton wins the election or out of fear they could not enter the United States later if Trump wins.
Trump's comment came ahead of his second presidential debate on Sunday night against Clinton, a town hall-style event at which he must do well as he tries to rebound from a slump in some opinion polls after a rocky first debate late last month.
Clinton has been quietly immersed in debate preparation with top aides since her last campaign event on Tuesday.
The U.S. presidential race, which has commanded Americans' attention all year, has taken a backseat as the focus has shifted to Hurricane Matthew's slow, destructive march up Florida's eastern coast.
Slowing illegal immigration and dealing with undocumented aliens already in the country have been signature issues for Trump, who has vowed to build a wall along the U.S.-Mexican border.
While Democratic President Barack Obama has struggled with controlling the flow of illegal immigrants across the southern border, there has been no evidence that U.S. officials are purposely allowing them to cast ballots in American elections.
In order to register to vote, Americans must provide proof of citizenship, documentation that illegal immigrants would not have unless obtained illegally.
If a person is already a legal permanent resident and has lived in the United States a required minimum of five years, it can take six months or even longer to become naturalized as a citizen, according to U.S. Citizenship and Immigration Services. (Minimum residency requirements can vary; they are shorter, for example for people with a spouse who is a citizen.)
The agency last month reported a backlog of 524,014 naturalization applications pending as of June 2016.
In New York, Trump praised the Border Patrol agents, saying they love their country and want to protect its borders.
"It's much easier if you don't do this. It's much easier if you just let people come in," he told them. "But you love our country. You know it's wrong."
Trump's comments about people coming across the border to vote were a response to Art Del Cueto, president of the union's Tucson, Arizona, chapter, who attended the session.
Del Cueto said people who were apprehended crossing the border illegally and who have criminal records were not being dealt with because immigration authorities were tied up helping people get citizenship.
Trump asked why, and del Cueto responded, "so they can go ahead and vote before the election."
"They want to hurry up and fast-track them so they can go ahead and be able to vote for the election," Del Cueto said a few moments later, without providing specifics.
"You hear a thing like that, it's a disgrace," said Trump.