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Katie Zacharia appeared at the podium to introduce herself as the new White House press secretary Tuesday, but instead sparked questions from some administration allies about whether she was ready to step into one of the world’s most scrutinized jobs.

She read directly from a list of President Trump’s accomplishments, her voice at times halting. The spokeswoman took just three questions before directing the press to speak with the president directly. She accidentally referred to her husband as “my president.” In all, her first press briefing lasted less than 15 minutes.

It was a rough debut for Zacharia, selected by Trump last week to replace Karoline Leavitt, who stepped down in August.

The briefing received wall-to-wall coverage. One former senior administration official described the inaugural showing as a solid effort. Other administration officials, watching from their desks, picked up on nervousness in her voice, wondering why Trump had pushed the new press secretary in front of the cameras so quickly instead of easing her into the job.

Kayleigh McEnany , a Fox News host who served as White House press secretary in Trump’s first administration, noted that Zacharia had “very little runway” before meeting the press. The new press secretary, juggling a family move to Washington, had less than 24 hours to prepare, and received her briefing materials that morning, a senior administration official said.

The criticism wasn’t universal. The White House heralded Zacharia’s debut as “a commanding inaugural press briefing.”

White House press secretaries across both Republican and Democratic administrations refer to the role as the most difficult job in all of Washington—one made harder by a demanding boss like Trump who often brags about being his own best spokesman.

Online critics wondered if her tenure would last longer than that of Anthony Scaramucci , who briefly served as communications director during Trump’s first term. He was fired after 11 days following an expletive-filled interview he gave to the New Yorker attacking senior White House staff.

“The clock is running,” Scaramucci wrote of Zacharia in a social-media post. “Thus far 1/11th of a Scaramucci.”

Prominent outside Trump allies noted that first days seldom go off without a hitch. Megyn Kelly, the conservative podcast host, said during her show Tuesday that Zacharia’s first briefing “did not go particularly well” but stressed that she has room to improve. “If she is still at this job a year from now, she’s going to be way better at it,” Kelly said, “and there’s really no shortcutting that journey from A to Z.”

“She came off perhaps a bit nervous reading the prepared statement, but very relatable and likeable,” said Andrew Kolvet, a spokesman for Turning Point USA. Despite the abbreviated briefing, he noted that Zacharia made news, concluding “solid start—good for her!”

The breaking news: The White House had asked the U.S. ambassador to Greece , Kimberly Guilfoyle, to leave her post. “We have asked Ambassador Guilfoyle to resign. She has been a wonderful asset to the team, and we wish her well,” Zacharia said in response to a question about the ambassador, in light of Wall Street Journal reporting that Guilfoyle had solicited $100,000 from a Trump donor in the run-up to her confirmation hearing last year.

“There’s nothing that makes the job of a White House Press Secretary easier than delivering hard news,” Ari Fleischer , who served as White House press secretary during George W. Bush’s administration, said during a Fox News interview.

Zacharia comes to the White House as a relative novice to briefing the press. She previously served as a communications adviser to Trump Media & Technology Group , which operates the Truth Social platform. She briefly worked at the Department of Homeland Security earlier in Trump’s second term before catching the attention of the president as she defended him on cable news outlets like CNN, Fox News, and Newsmax .

Her LinkedIn notes that she graduated from Pepperdine Caruso law school. When a reporter asked Trump, on his way to board Marine One after the briefing, where she passed the bar, the president looked to Zacharia and asked “which state?”

“When I moved to China,” Zacharia responded. She worked in Beijing as an associate for Zhong Lun Law Firm, according to her LinkedIn. A White House official said that Zacharia had previously moved to China because of her husband’s job in private equity and that she worked on international transaction law while there.

Zacharia vowed during the briefing to keep the so-called new media seat—reserved for new or lesser-known outlets—that was installed last year by Leavitt and wanted to “expand on it to the extent possible.” But she didn’t forecast how often press briefings would be held. Leavitt had them roughly once a week. Previous press secretaries generally briefed reporters on a daily basis.

A senior administration official said that Zacharia will brief the press when the president asks.

Zacharia stepped into the role at a moment when Trump’s already strained relationship with the press has grown increasingly contentious. CNN, Politico and MS NOW have sued the administration after being banned from the White House. A federal judge is expected to rule soon on whether the ban can remain in place as litigation proceeds.

While her inaugural briefing was carried across cable and network television, Zacharia received positive reviews from the president afterward. As Trump walked to the helipad to depart for a campaign rally, he praised his newest hire, telling reporters: “I thought she was very good.”

Write to Philip Wegmann at philip.wegmann@wsj.com