Former President George H.W. Bush said his son Jeb should run for president and blasted the New York Times for its "grossly unfair" criticism of another son, President George W. Bush.

During an interview on "FOX News Sunday," the nation's 41st president said Jeb, the former governor of Florida, is "as qualified and as able as anyone I know in the political scene" to be president.

"I'd like to see him run," Bush said. "I'd like to see him be president some day.

"As president, it's about service, service for the greatest country on the face of the Earth and the honor that goes with it," Bush said. "I think Jeb fits that description."

He added: "I mean, right now is probably a bad time, because we've got enough Bushes in there."

In the meantime, Jeb could take another job, his father suggested.

"If Jeb wants to run for the Senate from Florida, he ought to do it," Bush said. "He'd be an outstanding senator. This is a guy that really has a feel for people, the issues in Florida and nationally. And his political days ought not to be over, says his old father."

But the current President Bush's political days will soon be over, prompting the former President Bush to unburden himself about what he calls unfair criticism of his eldest son.

"It's been tough on his father and his mother," the ex-president said. We're not very good sports about sitting around and hearing him hammered, I think, unfairly.

"Now, there were some things that clearly he deserved criticism for," he said. "But I think the idea that everything that's a problem in this country should be put on his shoulders -- I don't think that's fair. And I'm not trying to get back in game by criticizing people, for example, the New York Times, but you know, it's just grossly unfair."

Bush said "it burns me up" when critics suggest he and his son are presidential rivals.

"There isn't any such competition," Bush said." We're very close, and we remained close for many, many years. People don't quite get that. But we are very close as father and son."

On Wednesday, Bush will join his son for a White House lunch that will also be attended by former Presidents Bill Clinton and Jimmy Carter, as well as President-elect Barack Obama. Bush does not know the incoming commander-in-chief well, but spoke highly of Obama.

"I talked to him right after the election and... assured him that he was my president," Bush said. "I've very impressed with his style on the campaign and his coolness and his articulate nature. I think he can give a sentence and it'll sound like it's been thought out by Shakespeare or something."

Bush said Obama should surround himself with people who "will not be out there talking to the press and... building their own nests." He also predicted that Obama's presidential honeymoon may be short lived.

"He should and will get people around him in whom he has their loyalty and to whom he can give his loyalty," Bush said. "But that'll change. Something will come up. Somebody will err. Something will come out of the unforeseen. This guy said that, he did that, and he'll have to move quickly to straighten that out."

Bush, known for skydiving well into his golden years, said he will "make one more parachute jump" in June, when he will be 85.

"Oh, there's a thrill with it," Bush enthused. "Just because you're an old guy, you don't need to sit around, sucking your thumb, drooling in the corner."

Bush said his "tears will be flowing" on Saturday, when the Navy commissions its newest aircraft carrier as the U.S.S. George H.W. Bush in honor of the former president, who was once the Navy's youngest pilot.

"It's very emotional to me and it's kind of the last big thing in my life," reflected Bush, who was shot down in the South Pacific during World War II. "This brings back a lot of memories. I mean, my going into the Navy at a young age was probably the best thing I ever did in my life. And then now to be, you might say, rewarded - certainly honored in this way - is just mind boggling."