McConnell's successor must work with Trump but 'stand his own ground,' Rounds says

Mitch McConnell's successor as Republican leader of the Senate must be able to both work with the next president, including if it's Donald Trump, and also "stand his own ground," Sen. Mike Rounds said Sunday.

Rounds, a South Dakota Republican, is backing colleague and fellow South Dakotan John Thune to take McConnell's role after the latter steps down in November. (Sens. John Barrasso and John Cornyn have either said they want the job or are expected to as well.)

"John Thune is the right guy at the right time. Great moral character," Rounds told ABC News "This Week" co-anchor Jonathan Karl, adding, "I think he will be independent enough to where -- he will look out also, just like Mitch did, for the institution of the Senate itself. So I'm optimistic."

McConnell, the longest-serving Senate leader in history, announced on Wednesday his decision to step down as his party's leader in November.

In his role, McConnell was a close legislative ally of Trump's while Trump was president -- including helping engineer the 6-3 conservative-leaning majority on the U.S. Supreme Court -- but broke with Trump over the events of Jan. 6 and has been repeatedly attacked by the Trump-led wing of the Republican Party.

More recently, the two have sharply divided on major issues like a bipartisan Senate immigration and foreign aid bill.

Rounds indicated on "This Week" that Senate Republicans going forward want to partner with Trump while maintaining their independence.

"We also know that we need leadership changes in the White House. And we're prepared for that. Whoever the [2024] Republican nominee is, we're going to get behind them and we're going to make sure that this thing happens where we get back to actually building this economy again," Rounds said.

Another priority will be the cost of living, he said.

Pressed by Karl on the role Trump will have in selecting the next GOP Senate leader, particularly given his criticism of McConnell and McConnell's allies like Thune, Rounds acknowledged that "he's going to have a voice in it, we recognize that."

"But we also know that in the Senate we've got a lot of independent thinkers ... The former president will have the opportunity to influence a number of my colleagues, but we also want to be able to have a good working relationship with him if he becomes the next president of the United States. We've got things we've got to get done," Rounds said.

"I think you're going to find that a lot of folks in the Senate will take their own time in terms of how they work through and, on a vote-by-vote basis, when they're going to support the president and when they're not," he added.

Karl noted that Rounds himself has been on the receiving end of some Trump attacks.

"I understand you say everybody needs to be on board in the general election, but how important is it to do what McConnell did, which is be willing to stand up to Trump?" Karl asked.

"That's what I'm looking for in a leader," Rounds said.

"As a Senate, our obligation is to look long term. We're elected from every single state and we want to take care of our individual states, but we've also got the bigger picture of constitutionally what is right and also, in terms of national defense, we've always got to be looking at national defense as our primary responsibility," he said.

Karl separately asked Rounds about Trump's legal argument that he should be granted complete immunity from prosecution for actions taken while he was president. The dispute is currently before the Supreme Court.

"Do you agree?" Karl asked.

"I do not," Rounds said.