A federal lawsuit by former Trump University students against the school’s founder, Donald J. Trump, will proceed toward trial, the judge in the case ruled on Tuesday.

In a written decision, Judge Gonzalo P. Curiel rejected a motion by Mr. Trump’s lawyers to dismiss the case, concluding that the aggrieved former students had raised a genuine question about whether Mr. Trump had “knowingly participated in a scheme to defraud.”

The case, in federal court in San Diego, has been a nagging concern for Mr. Trump’s Republican campaign for the presidency, as he pushes back against claims made by former students that his school cheated them out of their tuition by using high-pressure sales tactics and deceptive claims about what they would learn.

At one point, Mr. Trump publicly denounced the rulings of Judge Curiel, who was born in Indiana, and questioned whether he would be biased because of his Mexican heritage. Mr. Trump’s political opponents have repeatedly turned the case against him, including during the recent Democratic National Convention.