(CNN) President Donald Trump's July 20 meeting at the Pentagon was a "difficult and tense" session that focused on a wide range of US security interests, multiple senior US officials told CNN on Wednesday.

It was after that session that Secretary of State Rex Tillerson, in a private conversation with fellow US officials, exasperatedly called the President a "moron," a comment that sparked new questions about the two men's relationship.

Trump denied a rift on Wednesday, but officials described a fraught session over the summer with top national security officials that led to the secretary of state's insult.

The broad-reaching session, held inside the secure conference room known as the "tank," came a day after a White House situation room meeting on Afghanistan. Both meetings had been long scheduled to take place back-to-back.

The Pentagon briefing's focus was wider, however, ranging from various US treaty commitments to troop levels in different parts of the world to various other American interests, the sources said.

The White House meeting on Afghanistan had gone poorly, according to the sources. The President, displeased with the options he was being presented for managing America's longest war, suggested he wanted to fire the commander of US troops in Afghanistan, Army Gen. John Nicholson. And he compared the situation in the country to running a well-known Manhattan restaurant.

The meeting at the Pentagon a day later -- which had been scheduled for weeks -- was designed to give the President a broad tutorial on the global state-of-play, officials said. That's typical for meetings inside the Pentagon "tank," which are meant to give presidents a global overview of threats and commitments.

Some officials deemed the session particularly necessary, given Trump's demonstrated lack of understanding about the issues involved.

"It was a rough day and people weren't focused on what the secretary said, they were focused on what the President said," one of the officials said. "It was a rough session for the DOD people. They had their leadership questioned in a very direct way, and if anything came out from meeting, it was that."

The official said that after the set of meetings, participants were "ashen" at Trump's direct questioning of his commanders and his lack of a nuanced world-view. Meetings held inside the Pentagon "tank" are usually sobering looks at the realm of global threats.

Over the course of the session, there wasn't a discussion of increasing the US nuclear arsenal, according to three sources.

But Trump has said previously that he would push for scaling up US nuclear capability.

He said in a Reuters interview earlier this year that he wanted a world with no nuclear weapons, but worries the United States has "fallen behind on nuclear weapon capacity."

"I am the first one that would like to see ... nobody have nukes, but we're never going to fall behind any country even if it's a friendly country, we're never going to fall behind on nuclear power," he said. "It would be wonderful, a dream would be that no country would have nukes, but if countries are going to have nukes, we're going to be at the top of the pack."

In December, before he was sworn in as President, Trump expressed a similar sentiment on Twitter.

"The United States must greatly strengthen and expand its nuclear capability until such time as the world comes to its senses regarding nukes," he wrote.

Several White House officials on Wednesday denied an NBC News report that Trump called for a nearly tenfold increase in the nuclear arsenal during the heated meeting that ultimately led to Tillerson referring to the President as a "moron." CNN has not confirmed the NBC report.

Speaking in the Oval Office on Wednesday, Trump called that report "fake news."

"I never discussed it," Trump said ahead of talks with Canadian Prime Minister Justin Trudeau. "Right now we have so many nuclear weapons. I want them in perfect condition, perfect shape."

"When they said I want 10 times what we have right now, it's totally unnecessary, believe me," Trump continued. "It's got to be in tip-top shape."

And Trump denied a rift has developed between himself and Tillerson.

"We actually have a very good relationship," he said, going on to concede that his views on North Korea do differ from those of his top diplomat.

"I think I have a little bit different attitude on North Korea than other people might have. And I listen to everybody," he said. "But ultimately my attitude is the one that matters, isn't it? That's the way it works."