UNITED NATIONS (Reuters) - When President Donald Trump takes the world stage at the United Nations for the first time this week, he will share the spotlight with his envoy Nikki Haley, who has emerged as the surprising public face of U.S. foreign policy. Haley, the 45-year-old former South Carolina governor, has proven to be a high-profile member of Trump’s administration, at times overshadowing Secretary of State Rex Tillerson, the former chief executive of Exxon Mobil Corp, despite her lack of previous foreign policy experience, diplomats say. “For the U.S., Nikki Haley is remarkable. It’s hard to find in the Trump administration. It’s someone who is very approachable and politically very assertive,” said a senior European diplomat, speaking on condition of anonymity.  “I see her potentially taking over from Tillerson at some point. It’s clear her long-term objective is the presidency,” the diplomat said.  Haley dismisses speculation she could replace Tillerson, the country’s top diplomat, who has at times publicly differed with Trump during the president’s eight months in the White House. On Sunday, she told CNN that Tillerson is “not going anywhere and I continue to work well with him.” Trump’s speech on Tuesday at the U.N. General Assembly will be his highest profile opportunity to explain his foreign policy vision couched in his America First agenda. Haley arrived at the 193-member world body in January pledging to “take names” of allies who did not have Washington’s back. Trump administration officials say the president, happy with her performance, views her as both tough and smart. He speaks regularly with Haley, his fellow Republican, one U.S. administration official said.  Twice in five weeks she persuaded the 15-member U.N. Security Council to unanimously boost sanctions on North Korea. Her blunt language has raised eyebrows among diplomats. At the same time she has been careful not to steal the limelight from Trump, a wealthy businessman and former reality television star. “I personally think he slaps the right people, he hugs the right people, and he comes out with the U.S. being very strong in the end,” Haley told White House reporters on Friday. European Council on Foreign Relations U.N. expert Richard Gowan said Haley’s success could make Trump nervous and that it would be a “bad deal for her” if she was asked to replace Tillerson as secretary of state.   “She would lose the independence she enjoys in New York and (it would) tie her more closely to the president’s agenda. But it is an offer that she could not refuse. It’s an irony that the one way Trump can hurt Haley is to promote her,” he said.  Haley credits Trump with any U.S. achievements at the United Nations. After the Security Council toughened sanctions on North Korea this month, she praised his “strong relationship” with his Chinese counterpart for the result. When he dismissed the Sept. 11 U.N. resolution, which had been weakened by China and Russia, as “just another very small step, not a big deal,” Haley jumped to his defense and dismissed any suggestion they were not on the same page. “If we have to go further, this is going to look small compared to what we do,” she said at the time. Haley has made her mark also by fighting what she describes as U.N. anti-Israel bias, pushing for U.N. reform amid Trump’s call to slash U.S. funding, accusing Iran of meddling in the Middle East and challenging Russia over Ukraine and its support for Syrian President Bashar al-Assad. A senior administration official, speaking on condition of anonymity, said that during a National Security Council meeting on Iran this month, Trump specifically asked Haley’s opinion about what strategy to pursue. “She gave her opinion, and he liked her point of view,” the official said. “She wasn’t afraid to speak up.” A senior Iranian official, speaking on condition of anonymity, said, “This lady for some reason is very angry with Iran.” Before her selection as ambassador, Haley made national headlines when as governor she led a successful effort to remove the Confederate battle flag, viewed by many as a racist emblem, from the grounds of the South Carolina state capitol after the killing of nine black churchgoers in her state. During the 2016 presidential campaign Haley sparred with Trump, backing one of his rivals before he became the Republican candidate. The daughter of immigrants from India, Haley took Trump to task over his harsh campaign rhetoric about illegal immigration and for not speaking forcefully enough against white supremacists. When last month Trump inflamed tensions by saying that counter-protesters were also to blame for a deadly rally by white nationalists in Virginia, Haley spoke up, telling U.S. media she had a “personal conversation” with him about it.  Without naming Trump she wrote to staff at the U.S. mission to the United Nations to say that everyone must stand up and condemn hate. 