President Obama and Hillary Clinton are sharpening a joint line of attack against Donald Trump, accusing the GOP front-runner of lacking the intellect and temperament to be commander in chief.

Mrs. Clinton, who has yet to lock up the Democratic nomination, said Tuesday that Mr. Trump “has given no indication that he understands the gravity of the responsibilities that go with being commander in chief.”

“At some point, he’s going to have to be held to the standard we hold anybody running for president and commander in chief,” she said on MSNBC. “What is it you’re proposing to do as president and commander in chief? So far we haven’t seen any of that. We’ve seen a lot of rhetoric, we’ve seen a lot of insults.”

SEE ALSO: Clinton: Trump doesn’t understand ‘gravity of the responsibilities’ of being president

Her criticism of Mr. Trump’s qualifications to be commander in chief came on the same day that the New York real estate mogul cemented his status as the presumptive GOP nominee with a victory in the Indiana primary over Sen. Ted Cruz of Texas.

Mrs. Clinton’s characterization of Mr. Trump as recklessly unfit to lead also came just hours after Mr. Obama delivered his broadest dig yet at the Republican front-runner, on the same theme.

“He is not somebody who, even within the Republican Party, can be considered as equipped to deal with the problems of this office,” Mr. Obama told an ABC-affiliate in New Hampshire in an interview.

SEE ALSO: Trump dominates TV news, draws 3 times as much coverage as Cruz, 15 times more than Kasich

White House press secretary Josh Earnest refused to elaborate Tuesday on what the president meant by “equipped.” He said Mr. Obama “is referring to judgment that, ultimately, the American people will have to make.”

MoveOn.org, a progressive digital organizing group, also announced that it will be running a multimillion dollar campaign to keep Mr. Trump out of the White House, and is already testing messages in key states.

“Donald Trump, the now-presumptive Republican nominee, and his hateful and bigoted rhetoric are not only a political threat but a clear and present danger to the very fabric of our nation,” said Ilya Sheyman, MoveOn.org Political Action executive director, in a statement.

The Democratic National Committee, essentially a campaign arm of the White House, joined the blitz against Mr. Trump Tuesday, calling him “Dangerous Donald.” It accused him of “just spouting nonsense he reads on the Internet or in the tabloids,” including theories that Supreme Court Justice Antonin Scalia was murdered, that vaccines cause autism and that Mr. Obama wasn’t born in Hawaii.

“The fact that he has even considered any of these theories proves that once again, Dangerous Donald lacks the judgment and temperament to serve as president,” the DNC said.

A Democratic operative with ties to the White House called the development “the beginning of a two-pronged strategy.”

“The Clinton campaign — and the president as well — will try to take the high road to the extent they can and focus on Trump’s lack of qualification to be the next commander in chief, while leaving the attack-dog stuff to third party groups and other surrogates,” the Democrat said.

Republican consultant John Feehery said the Democrats’ strategy actually highlights a potential weakness for Mrs. Clinton in the fall.

“This is a change election, and Hillary Clinton is the status quo candidate,” Mr. Feehery said. “She is campaigning as the responsible candidate. The country is not really taking that argument that seriously this year. You can make the case that experience might be a little overrated with this electorate.”

Mrs. Clinton’s foreign policy experience as secretary of state obviously didn’t matter to legions of Democratic voters who have favored Sen. Bernard Sanders of Vermont in the primary, Mr. Feehery said. And Mr. Trump’s lack of government experience hasn’t bothered millions of Republican primary voters who have put him within reach of capturing the GOP nomination.

“The problem with Hillary’s experience is it wasn’t all that positive,” Mr. Feehery said. “It wasn’t like she magnificently handled Libya. That was a blunder.”

He added, “People want change. That’s what [Democrats] are grappling with. The Democrats know to run against Ted Cruz, but they’re not sure how to run against Donald Trump. They’re going to call Trump dangerous, they’re going to call him a racist, they’re going to call him a misogynist. And they’re going to see what sticks.”

Mr. Trump said he’s had plenty of foreign policy experience from operating his business empire.

“I do deal with leaders around the world,” he said on the eve of the Indiana primary. “I built a great company and right now we have hundreds of deals being negotiated all over the world by my company and I deal with presidents and I deal with prime ministers and I deal with everybody. I probably have more experience than virtually anybody looking at this office.”

The president made several jokes at Mr. Trump’s expense Saturday night at the annual White House Correspondents’ Dinner.

“They say Donald lacks the foreign policy experience to be president. But in fairness he has spent years meeting with leaders from around the world: Miss Sweden, Miss Argentina, Miss Azerbaijan,” the president said.

Of the president’s mocking his foreign policy experience at the correspondents’ dinner, Mr. Trump told CNN, “I thought it was fine, honestly I’ve heard it, I’ve heard it before.”

If Mr. Trump does become the GOP nominee, Mr. Obama said he’s confident that the Democratic nominee will win in November.

“If in fact the Republicans nominate Mr. Trump, then it’s going to be an interesting fall season,” he told WMUR. “I’m confident that ultimately the Democrat in that circumstance will win.”

As the White House this week marked the fifth anniversary of the killing of Osama bin Laden, Mr. Obama also was asked by CNN if he has considered Mr. Trump making a similar decision to approve a special forces mission.

“I don’t have those thoughts, because I don’t expect that to happen,” the president said.