President Donald Trump called the Artemis II astronauts after the historic lunar flyby on Monday and invited them to the Oval Office upon their return to Earth.

“Today you’ve made history and made all America really proud, incredibly proud,” Trump said. “We have a lot of things to be proud of lately, but this is, there’s nothing like what you’re doing circling around the moon for the first time in more than half a century and breaking the all-time record for the farthest distance from planet Earth.”

After inviting the astronauts to visit the White House, Trump said, "I’ll ask for your autograph ... I don’t really ask for autographs much, but you deserve that."

"I look forward to having you in the Oval Office at the White House, and we will celebrate your incredible achievements and trials," the president said.

The president also said the U.S. will “establish a permanent presence on the moon” one day in the future, as well as “push on to Mars,” though he recognized that the latter feat may not necessarily occur during his administration. 

“We'll plant our flag once again, and this time we won't just leave footprints, we'll establish a permanent presence on the moon, and we'll push on to Mars, that'll be very exciting. I'm waiting for that so much. I'd love to be here, but maybe we won't quite make it in terms of timing,” Trump said.

The total solar eclipse has ended and the lunar flyby has concluded, NASA said. The Artemis II crew is now beginning the return trip home.

On Tuesday, the Orion spacecraft will exit the lunar sphere of influence at approximately 1:25 p.m. ET -- about 41,072 miles from the moon, according to the space agency.

The Artemis II crew named a crater on the moon, sitting on the boundary of the near side and far side, after mission commander Reid Wiseman’s late wife, Carroll.

Carroll Wiseman passed away in 2020 after a five-year battle with cancer, according to her obituary.

"We lost a loved one. Her name was Carroll. The spouse of Reid, the mother of Katie and Ellie," Canadian Space Agency astronaut and mission specialist Jeremy Hansen said earlier on Monday, tearing up. "It's a bright spot on the moon. And we would like to call it Carroll."

The crew shared a long group hug afterwards.

For another crater on the far side of the moon, Hansen said the crew would like to name it "Integrity," in honor of the name the astronauts have given the spacecraft that carried them farther into space than any other human in history.

-ABC News' Briana Alvarado

The Artemis II astronauts sent back descriptions of the total solar eclipse they viewed from space to NASA's Mission Control.

"It’s truly hard to describe. It is amazing," pilot Victor Glover said.

Glover said that the Orion spacecraft was made as dark as possible due to every bit of light in the cabin affecting the view.

"It’s a wicked view," he said of the darkened moon with deep space behind it.

"It’s indescribable," commander Reid Wiseman added. "No matter how long we look at this our brains are not processing this image in front of us. It is absolutely spectacular, surreal, there’s no adjectives. I’m gonna need to invent some new ones to describe what we’re looking at right now."

During Friday's press conference, NASA leaders gave a preview of the Artemis II crew's upcoming lunar flyby.

On Saturday, the crew will take a selfie of the spacecraft and test some thruster flight modes on Orion.

On Monday, during the six-hour lunar observation period when the crew is on the far side of the moon, the astronauts will be at their closest approach to the lunar surface.

They will be making visual observations as well as photographs and video. The observation period will begin at around 2:30 p.m. ET, NASA said.

The blackout period, when the crew is behind the moon and loses communications with Mission Control, is expected to last about 40 minutes.

When asked if there is reason to worry about the astronauts when they are behind the moon and out of contact with Earth, Judd Frieling, Artemis flight director, said, "Physics takes over and physics will absolutely get us back to the front side of the moon."

-ABC News' Matthew Glasser