A leading Republican congressman on Sunday said that the process behind the House impeachment probe of President Donald Trump is just as important as the case itself because "there's a reason we let murderers and robbers and rapists go free when their due process rights have been violated."

The comments from Rep. Mac Thornberry, R-Texas, came as Republicans and Democrats dominated the airwaves Sunday morning with discussion of the president's conduct toward Ukraine, which is at the center of the investigation. Multiple Trump administration officials have testified on the record that they believed Trump was withholding roughly $400 million in military aid to the country until Ukrainian leadership publicly announced investigations into the Bidens and Democrats.

"I believe it's inappropriate for a president to ask a foreign leader to investigate a political rival," Thornberry, ranking member on the House Armed Services Committee, told ABC's "This Week." "Now that leads to a question if there's a political rival with a family member who is involved in questionable activity, what do you do? Just let them alone? But set that aside. I believe it was inappropriate. I do not believe it was impeachable."

Asked why Republicans appear to be focused on process over the substance of the allegations facing the president — that he leveraged the power of the presidency to have a foreign nation investigate political opponents — Thornberry said, "There's a reason we let murderers and robbers and rapists go free when their due process rights have been violated."

"We believe the integrity of the system, the integrity of the constitution, the integrity of the processes under our legal system, is more important than the outcome of one particular case," he continued. "So, I don't think you can sweep process under the rug because it is part of an impeachment decision, which has a constitutional requirement: bribery, treason, high crimes and misdemeanors, but also a political element about whether it's good for the country to pursue it under these circumstances."

He added that what Trump is accused of doing doesn't sound much different than conduct he's engaged in throughout his presidency.

"So, is there some sort of abuse of power that rises to that threshold that is different than the American people have been hearing for three years?" Thornberry said. "I don't hear that."

Trump responded later Sunday, telling Republicans not to "be led into the fools trap of saying it was not perfect, but is not impeachable. No, it is much stronger than that. NOTHING WAS DONE WRONG!"

The call to the Ukrainian President was PERFECT. Read the Transcript! There was NOTHING said that was in any way wrong. Republicans, don’t be led into the fools trap of saying it was not perfect, but is not impeachable. No, it is much stronger than that. NOTHING WAS DONE WRONG! — Donald J. Trump (@realDonaldTrump) November 10, 2019

Speaking with CBS's "Face the Nation," Sen. John Kennedy, R-La., said the debate over whether Trump engaged in a "quid pro quo" — which Trump insists he did not — is "a red herring."

Kennedy said Trump either "asked for an investigation of a political rival" or "asked for an investigation of possible corruption by someone who happens to be a political rival."

"The latter would be in the national interest, the former would be in the president's parochial interest and would be over the line," he said. "I think this case is going to come down to the president's intent, his motive, did he have a culpable state of mind."

Democrats, meanwhile, said the evidence presented so far in the impeachment probe amount validated the idea that Trump engaged in an "extortion scheme." Public hearings in the investigation begin this week.

"It's important that the president has due process and evidence is not a conclusion," Rep. Eric Swalwell, D-Calif., told "Face the Nation." "We have enough evidence from the depositions that we've done to warrant bringing this forward, evidence of an extortion scheme using taxpayer dollars to ask a foreign government to investigate the president's opponent. But it's important that these witnesses raise their right hands and take questions from both Republicans and Democrats. The president is going to get that."

Asked what makes the Ukraine investigation different from former special counsel Robert Mueller's investigation, Rep. Jackie Speier, D-Calif., said this time, Trump's conduct "is a very simple, straightforward act."

"The president broke the law," she said. "He went on a telephone call with the president of Ukraine and said I have a favor, though, and then proceeded to ask for an investigation of his rival. And this is a very strong case of bribery, because you have an elected official, the president, demanding action of a foreign country in this case, and providing something of value, which is the investigation, and he is withholding aid, which is that official act.

"And the constitution is very clear: treason, bribery or acts of omission," she continued. "In this case, it's clearly one of those."