President-elect Donald Trump signaled Tuesday he’s still looking for ways to discourage those who burn the American flag and then shield themselves in their free speech rights.

“We’ll see what we’re going to do about that,” Mr. Trump said as he rallied with supporters in Fayetteville, North Carolina, to thank them for the state backing him in last month’s election.

Mr. Trump also officially introduced retired Marine Corps Gen. James N. “Mad Dog” Mattis as his pick to run the Defense Department, saying he’ll oversee a revamp of the military that modernizes equipment even as it pulls back American commitments overseas.

“Mad Dog plays no games, right?” Mr. Trump said.

He also warned Democrats not to try to use a law prohibiting recently retired military officers from serving as Defense secretary. Republicans in Congress are planning to pass a waiver allowing Gen. Mattis to serve notwithstanding the law.

Democrats have said there should be a full debate on whether that would ruin the tradition of civilian control of the military — and hope to use the fight to delay Mr. Trump’s nominees, as retaliation against the GOP for its treatment of President Obama’s picks.

Mr. Trump said he would have none of that.

“Oh, if he didn’t get waiver there’d be a lot of angry people,” Mr. Trump said.

For his part Gen. Mattis, despite a career in the military, pledged to uphold the traditions of civilian leadership.

“I look forward to be the civilian leader, so long as Congress gives me the waiver,” he said.

The military-heavy remarks were aimed at Fort Bragg, a North Carolina institution that’s home to Army Special Operations Command.

Mr. Trump kicked off his speech by reprising a fight last week over flag-burning.

He tweeted that those who burned the flag should face a penalty, including jail time or loss of citizenship.

The Supreme Court has ruled flag burning is protected speech under the Constitution, and efforts in Congress to pass an amendment to outlaw flag burning have gone nowhere.

Mr. Trump didn’t list any specific punishments Tuesday, but signaled he still wants to do something.

“We will respect people’s rights, we will respect constitutional rights, and for all America, we will respect our great American flag again, believe me,” he said.