Donald Trump Jr. said Tuesday in an interview on "CBS This Morning" that "there are very few people" his father can "fully trust." "Now, there are people that are doing great jobs," he said. "I think Mike Pompeo's doing a great job. I think a lot of his Cabinet's doing a very good job."

Trump Jr. also said President Trump's personal attorney, Rudy Giuliani, is "doing a good job." "I think it's different in that my father's a fighter, right? And so is Rudy," Trump Jr. said.

Federal investigators are looking into Giuliani's involvement with two of his associates who were indicted for campaign finance violations. He was also named in the House impeachment inquiry testimony of former U.S. ambassador to Ukraine, Marie Yovanovitch. In the transcripts released Monday, Yovanovitch said Giuliani worked to have her removed from her post.

Trump Jr. also addressed his recent claims that Hunter Biden tried to benefit financially from his father's position as vice president.

"CBS This Morning" co-host Anthony Mason asked him, "Aren't you benefiting essentially from your father being president?"

"Not even a little bit, from that, from the politics. I've benefited from my father's name. I'm not going to hide from that. So has Hunter. I even can't fault him for that," Trump Jr. responded. But Trump Jr. said his family business "stopped doing new deals" since his father took the presidency.

Trump Jr. was promoting his new book, "Triggered: How the Left Thrives on Hate and Wants to Silence Us."

On Ivanka Trump, Jared Kushner, and Rudy Giuliani

GAYLE KING: We know that your father operates on his instinct and his gut. Outside of himself, who do you think – whose advice do you think he respects and trusts the most?

DONALD TRUMP JR.: Listen, I think without question, Jared and Ivanka are doing an amazing job. I think they're getting things done. And I think, you know, there are very few people that he can fully trust. Now there are people doing great jobs. I think Mike Pompeo's doing a great job. I think a lot of his Cabinet's doing a very good job.

ANTHONY MASON: Is Rudy Giuliani doing a good job?

TRUMP JR.: I think in his role, he's outside of government that way. But in his role, I think he's doing a good job.

KING: He seems to be creating more problems for the Trump administration.

TRUMP JR.: Again, I think it's different in that my father's a fighter, right? And so is Rudy. And I think the reality is this: My father has shown Republicans it's okay to fight back. We've turned the other cheek as conservatives for 50 years. And all it's done is allowed us to cede ground. We have to fight back the same way the Democrats fight. And I think my father does that, and I think that creates a lot of controversy because people aren't used to it.

On criticism of Hunter Biden

TRUMP JR.: I've benefited from my father's name. I'm not going to hide from that. So has Hunter. I even can't fault him for that. There's a difference, though, when Hunter Biden's getting board seats, coming back with $1.5 billion from China, because of his father's taxpayer-funded office. Hunter Biden knows nothing about energy, never invested in it in his life. He gets a board in a company, a corrupt Ukrainian oil company, in a language he doesn't speak because his father's handling that region. We were international business people. Gayle, you can vouch for that, for decades, and more importantly, we stopped doing new deals. We have deals that we were obligated to finish that we signed up in 2010.

MASON: But you have expanded some of those deals. You're expanding in Scotland, you've traveled to India, to Indonesia.

TRUMP JR. We have to finish out the deals that we have that are existing. We have literally a contractual – we have not signed a new deal abroad since my father took the presidency. Now we'd be able to legally. We chose not to and did that publicly, so as not to even create the notion of impropriety. We didn't magically become international business people because of my father's office. We frankly stopped our international expansion because of it. And that's a big distinction that the media really likes to neglect.

On the country's political divide

DOKOUPIL: The thing that everyone seems to agree on in this country is that the temperature is too high. People on all sides of the political persuasion, they say that. Do you agree that the temperature is too high in this country, that we're too divided? And if so, what are you doing to heal that divide? 'Cause it seems like you're doing the opposite.

TRUMP JR.: Listen, I'd love to see it get back to a place of normalcy. I don't know that that exists today. I mean, I think when I look at what's going on, when I look at sort of the media bias, when I look at those things, it makes it very hard for my father to do his job. For example, last weekend, al-Baghdadi, the leader and founder of ISIS [was killed]...you can't say, "Hey, we should get back to normal," when the Washington Post is going around and calling the leader of ISIS, a guy that lit people on fire in cages, who throws homosexuals off buildings is an austere religious scholar. You know, you need some grown-ups in the room there, too, because that's not working.

DOKOUPIL: I'm asking you if you're interested in any kind of healing rhetoric that might bring the country closer together and you're picking a fight with the Washington Post.

TRUMP JR.: I think we're actually all pretty let -- live and let live. So is my father. But today, you know, it's sort of the "woke" goalposts. They keep moving. The example I use in the book is obviously as it relates to, you know, trans women in sports. Identify how you want. I think it's wonderful. I don't care. When you start saying, "Okay, I'm a man. I've become a woman. I'm now winning national championships, setting weightlifting world records," you know, displacing women who've worked their entire lives to get to a point in their careers, I think that's wrong. And that's the point. The goalposts never stop moving.

On running for office

MASON: Are you interested in running for political office?

TRUMP JR.: I'm interested in winning 2020 for my father right now. We'll worry about everything else later.

KING: No, no, no, in the book you said, listen, I never thought I'd be in politics, I never thought I'd be a vegan, but now, you admit that you've got the political bug.

TRUMP JR.: But I won't be a vegan, I promise you.

MASON: Do you see yourself running for office?

TRUMP JR.: Listen, I don't ever rule anything out. The reality is this. Right now, I like the campaigning part. I actually enjoy some of that fight. I like getting out there and being with real people and seeing the difference that my father and his policies are making in their lives. I don't know right now at this stage of my life that I would like the day job component of it.