United States President Donald Trump speaks with U.S. Ambassador to the United Nations Nikki Haley before a meeting during the United Nations General Assembly at U.N. headquarters Monday. (Seth Wenig/AP)

President Trump's two most high-profile diplomats, Rex Tillerson and Nikki Haley, were with him at a meeting with African leaders here this week when the president took the lectern to offer a big reveal.

He had decided to dispatch one of them to a new on-the-ground peace mission in violence-plagued South Sudan and Congo.

"I'm sending Ambassador Nikki Haley," Trump declared.

That the president gave the nod to Haley, his United Nations envoy, and not Tillerson, the secretary of state, who outranks her as a member of the Cabinet, was not necessarily evidence, in and of itself, that she was upstaging him.

But Haley's prominence at Trump's side through four days of meetings at the annual U.N. General Assembly this week continued a rapid and remarkable rise for the former South Carolina governor, and highlighted her growing influence and ambition within an administration struggling to project a coherent foreign policy.

As Trump made his debut in the global spotlight, he was accompanied nearly as often by Haley as by administration officials like Tillerson who are technically higher in the pecking order. Back in Washington, Haley's rising profile has led to speculation that she would be a potential replacement for Tillerson if the increasingly isolated State Department chief were to step aside. Haley has vehemently rejected the idea, saying repeatedly that she is not considering such a move and that Tillerson is not planning to leave.

"There's going to be chatter about things," she said at a news briefing here Thursday when asked about speculation about her future.

"What I'm trying to do is do a good job," she said. "I'm trying to serve the president and the country the best I can. If people want to take it as anything else, that's not something I spend time on."

Tillerson was asked about the palace coup rumors during a television appearance Friday.

"I think we have a secretary of state, and I think he's planning to hang around," a smiling Tillerson said on ABC's "Good Morning America."

It's not that Tillerson was missing in action here; he accompanied Trump to numerous events and held meetings with foreign delegations, including blunt discussions with the Iranians over Trump's sharp criticism of the U.N.-backed nuclear deal. The president appears to be leaning toward declaring Tehran in violation of the agreement before a certification deadline next month.

President Trump speaks as Secretary of State Rex Tillerson, center, and Ambassador to the U.N. Nikki Haley sit at his side during a working dinner with Latin American leaders Monday. (Kevin Lamarque/Reuters)

But it was Haley and national security adviser H.R. McMaster, not Tillerson, who previewed the trip for reporters in the White House briefing room. And it was Haley who introduced Trump on Monday at the United Nations' opening session on internal reforms, touting his "businessman's eye" for seeing potential in the world body that Trump had criticized as ineffectual during his campaign.

To outside observers, the differences between Haley, a former politician, and Tillerson, former ExxonMobil chief executive, have been stark. Although she came to the job with virtually no foreign policy experience, Haley has worked hard to establish relationships with foreign officials and journalists, while Tillerson has exhibited a sense of isolation within his own department and has kicked most of the State Department reporters off his government jet.

"Nikki is a politician and has worked as a politician her whole life," said Ian Bremmer, president of the Eurasia Group, a global risk-assessment firm. "She's more flexible and willing to be charismatic. The lack of experience has not hurt her."

Haley's influence within the administration has emerged in surprising ways for a onetime critic of Trump whose foreign policy and national security views hewed to mainstream conservatism.

She is an interpreter for Trump's "America first" agenda at the United Nations and has ­become a frequent presence on political talk shows, emerging as the loudest administration voice, outside the president himself, in criticizing the Iran accord. Despite nearly universal support for the Iran deal among her U.N. colleagues, Haley has become the megaphone for Trump's deep suspicions about the landmark agreement negotiated by his predecessor, Barack Obama.

She has advised Trump about how he could back away from the deal next month on grounds she can defend at the United Nations, people familiar with the matter said.

"This situation is not an easy situation by any means," she said. Citing past nuclear-related deals with North Korea that were violated as Pyongyang acquired nuclear and ballistic missile capabilities, Haley said: "Here we are again. We do not want to be dealing with the next North Korea."

It was Haley who spearheaded U.S. efforts to persuade the United Nations to enact two recent rounds of tough economic sanctions on North Korea. The task required some tricky diplomacy with China and Russia, and won admiration among important U.S. allies.

At the same time, her contention during a Security Council session that North Korea is "begging for war" provoked a round of eye-rolling from some foreign diplomats, who saw her comments as a needlessly bellicose echo of Trump's amped-up language.

But Haley has made an impression at the United Nations, joking about using her high heels to kick opponents in the shin. And for a Trump administration that has been criticized for a lack of minorities and general hostility to foreigners, Haley, the U.S.-born daughter of Indian immigrants, offers a prominent public face of diversity.

She is widely viewed within the GOP as a future presidential candidate.

Tillerson, by contrast, has found himself on the losing side of key internal policy arguments, most notably over the fate of the Iran nuclear deal and the Paris climate accord.

The U.N. job has given Haley a Cabinet-level post outside the daily political combat in Washington.

Her fierce denunciation of what she calls systemic bias against Israel at the United Nations has made her the darling of Israeli hawks and raised her star with pro-Israel Republicans in America.

"When you have a former politician at the U.N., it's an advantage," said Israeli U.N. Ambassador Danny Danon, also a former politician. "When you know how to get things done, when you know the practical aspects, I think it's a difference and it's better."

After Haley professed Thursday not to worry about public talk about her ambitions, a reporter followed up: "Do you want to be secretary of state?"

"No, I do not," she replied.