Trump admin live updates: Trump says Hamas will release hostage Edan Alexander

Secretary of Defense Pete Hegseth on Tuesday did not hint at the U.S. standing down on the Houthis or discuss ongoing operations when he spoke at an annual conference in Tampa, Florida, focused on special operations forces.

Instead, Hegseth spoke only in general terms of Trump's goal was to re-establish deterrence around the world.

In a speech, Hegseth talked about raising "combat standards."

"They have to believe that America is strong, that peace through strength is real," Hegseth said in his speech.

"No more pronouns, no more climate change obsession, no more emergency vaccine mandates, no more dudes in dresses. We're done with that s---," he said.

-ABC News' Anne Flaherty

The Houthis are not immediately agreeing to the U.S. proposed ceasefire, according to a Houthi official.

The Houthis will "evaluate" the U.S. ceasefire proposal “on the ground first,” Mohammed Ali al-Houthi, a member of the Houthi Supreme Political Council, said in a post on X.

"Yemen operations were and still are a support for Gaza to stop the aggression and bring in aid," he said in his post.

-ABC News' Ellie Kaufman

A ceasefire agreement between the Houthis and the US has been reached, a spokesman for the Foreign Ministry of Oman said in a post on X Tuesday after Trump’s comments on the matter.

“Following recent discussions and contacts conducted by the Sultanate of Oman with the United States and the relevant authorities in Sana’a, in the Republic of Yemen, with the aim of de-escalation, efforts have resulted in a ceasefire agreement between the two sides,” the statement from the Foreign Ministry of Oman said.

“In the future, neither side will target the other, including American vessels, in the Red Sea and Bab al-Mandab Strait, ensuring freedom of navigation and the smooth flow of international commercial shipping,” the statement added.

-ABC News' Ellie Kaufman

The Supreme Court ruled Tuesday that the Trump administration can move forward with a ban on transgender military service members for now, lifting a lower court injunction against the policy after a judge ruled it was an "unsupported, dramatic and facially unfair exclusionary policy."

The court did not explain its decision other than to say the order would expire if the justices ultimately take up the case on the merits and issue a ruling striking it down. Litigation continues in the Ninth Circuit Court of Appeals.

Justices Sonia Sotomayor, Elena Kagan and Ketanji Brown Jackson indicated they would have denied Trump's request for a stay.

-ABC News' Devin Dwyer