CONROE, Texas — Donald J. Trump said on Saturday that if elected to a new term as president, he would consider pardoning those prosecuted for attacking the United States Capitol on Jan. 6 last year.

He also called on his supporters to mount large protests in Atlanta and New York if prosecutors in those cities, who are investigating him and his businesses, took action against him.

The promise to consider pardons is the furthest Mr. Trump has gone in expressing support for the Jan. 6 defendants.

“If I run and I win, we will treat those people from Jan. 6 fairly,” he said, addressing a crowd at a fairground in Conroe, outside Houston, that appeared to number in the tens of thousands. “We will treat them fairly,” he repeated. “And if it requires pardons, we will give them pardons, because they are being treated so unfairly.”

At least 700 people have been arrested in connection with the Jan. 6 riot, including 11 who have been charged with seditious conspiracy. Some have said they believed they were doing Mr. Trump’s bidding.

As president, Mr. Trump pardoned a number of his supporters and former aides, including Michael T. Flynn, his first national security adviser, who twice pleaded guilty to lying to the F.B.I., and Stephen K. Bannon, his former campaign strategist and White House adviser, who was charged with defrauding donors to a privately funded effort to build a wall along the Mexican border.

Late Sunday, Mr. Trump issued a statement denouncing a bipartisan effort to rewrite the Electoral Count Act of 1887, a century-old law that the former president and his allies misinterpreted in their failed effort to persuade his vice president, Mike Pence, to throw out legitimate election results. The effort to change the law is aimed at preventing any similar attempts in the future by clarifying that the vice president does not have the power to overturn results.

“Mike Pence did have the right to change the outcome, and they now want to take that right away,” Mr. Trump said. “Unfortunately, he didn’t exercise that power, he could have overturned the election!”

The statement was the first time Mr. Trump described his goal as overturning an election. But Mr. Trump’s statement also included his usual false assertions about election fraud, suggesting he does not believe the election was legitimate.

The statement signifies an increase in the intensity of the former president’s push to litigate the 2020 election and comes days after Senator Mitch McConnell, the minority leader, issued a public warning to Republican candidates to “respect the results of our democratic process” during an interview with CNN.

Members of both parties rebuked Mr. Trump’s pardon remarks on Sunday, including lawmakers who fled the rioters as they breached the Capitol and the Senate chamber. Max Rose, a Democrat looking to reclaim his New York seat from Representative Nicole Malliotakis, one of the Republicans who voted to overturn the election results, called on his opponent to condemn the remarks.

“If Congresswoman Malliotakis truly cares about America, she must not only denounce Donald Trump’s promise to these insurrectionists, but make it clear that their convictions are just,” Mr. Rose said in a statement.

Senator Susan Collins of Maine, one of seven Republicans who voted to convict Mr. Trump in his second impeachment trial for incitement of an insurrection, said on ABC’s “This Week” on Sunday that she did not think the former president should have made the comments, adding, “We should let the judicial process proceed.”

Senator Lindsey Graham of South Carolina, a Republican who has re-emerged as an ally to the former president after condemning him in the aftermath of the Jan. 6 riot, called the remarks “inappropriate.”

“I don’t want to reinforce that defiling the Capitol is OK,” Mr. Graham said, speaking on CBS’s “Face the Nation.” “I don’t want to do anything that would make this more likely in the future.”

In his speech on Saturday, Mr. Trump also took aim at the New York State attorney general and the Manhattan district attorney, both of whom have been investigating his businesses for possible fraud, and at the district attorney in Fulton County, Ga., who is empaneling a special grand jury to investigate Mr. Trump’s efforts to overturn the 2020 election results in that state.

He urged his supporters to organize large protests in New York and Atlanta, as well as in Washington, if those investigations led to action against him.

“If these radical, vicious, racist prosecutors do anything wrong or corrupt,” he said, “we are going to have in this country the biggest protests we have ever had.”

The event in Conroe drew Trump supporters from across Texas and as far away as New Jersey and Washington State, some of whom had camped out at the fairground for several days. For much of Saturday, a festive atmosphere prevailed, with billowing flags and omnipresent T-shirts declaring “Trump 2024.”

As his speech stretched on past an hour, Mr. Trump’s rhetoric grew more pointed, and his attacks on the news media more belabored. “The press is the enemy of the people,” he said, prompting angry boos. He added, “The corrupt media will destroy our country.”

Reid J. Epstein contributed reporting.