The administration has a list of names and Mr Trump expected a decision in "two or three weeks" in naming a successor. "Thank you for standing with the truth without fear".
Before being chosen as Trump's ambassador, Haley, 46, served as governor of the state of SC - the first woman to hold the post.
Haley, the former governor of SC, has been a fierce advocate for Trump's policies at the U.N. She said Tuesday that in the past two years, the US had become respected on the world stage, if not necessarily liked. "I look forward to working with her for the rest of the year". I mean, does this bootlicking sound like someone mounting a primary challenge?
She has been more outspoken in calling out Russian aggression than Trump, for example. "She's made it a more important - more importantly, a more important position".More news: Michael strengthens into a hurricane, menaces Florida
Ms Haley's resignation is the latest shake-up in the turbulent administration, coming just weeks before the November midterm elections.
Haley, the former governor of SC, was a critic of Trump's during the 2016 Republican primaries and endorsed his opponent Sen.
In April, Mrs Haley clashed with the White House when a Trump aide suggested she had prematurely announced a round of sanctions against Russian Federation. After running for the SC legislature in 2004, Haley, who is married to U.S National Guard office, became only the second Indian-American government of a U.S state (after Bobby Jindal) in 2010.
Ivanka was in the White House to listen to Haley explain how she will depart her role at the end of the year. Then he'll run her as VP in 2020.
The resignation will take effect at the end of the year, Trump and Haley said.More news: China says Interpol chief being probed on suspicion of violating the law
"As a strong supporter of term limits, I have long believed that rotation in office benefits the public", she said in her resignation letter to Trump, which was dated October 3.
"But I don't agree with the president on everything".
"We're all happy for you in one way, but we hate to lose (you)..."
"Countries may not like what we do but they respect what we do", she said, echoing the president's often-stated aim to make the United States a more muscular presence on the global stage. "It's something that we don't stand for in America". He allowed her to address reporters from the Oval Office, a departure from the abrupt tweets Trump often uses to announce high-level staff changes. "Now, the United States is respected", Haley told reporters at the White House.More news: Interpol asks China for information on its missing president