Trump said there are "many good people" who want the position at the United Nations and said he and Haley would be looking at who he will select for her successor.
Trump did said Haley would help him make the final pick for her replacement.
She gave no reason for her departure after two years, though there has been speculation she will return to government or politics at some point.
Before being chosen as Trump's ambassador, Haley, 46, served as governor of the state of SC - the first woman to hold the post.
At the United Nations, she helped spearhead the administration's efforts to combat what it alleged to be anti-American and anti-Israel actions by the global body, including the USA decision to leave the Human Rights Council and to stop funding the United Nations agency for Palestinian Refugees, known as UNRWA.
There is no evidence, however, that the scrutiny of those flights had anything to do with Haley's decision to leave her diplomatic post.
Yet it's often said that the UN's biggest peacekeeping mission is directed against the Trump White House, and Mrs Haley was seen as a valuable ally.
At the U.N., Haley helped spearhead the Trump administration's efforts to combat what it alleged to be anti-American and anti-Israel actions by the worldwide body.
"I am such a lucky girl to have been able to lead the state that raised me, and to serve a country I love so very much".
'Ambassador Haley asserted that each flight qualified for an exception to the rules for gifts based on personal relationships with the donors, ' according to the letter.
"No, I am not running in 2020", Haley said, adding that she will campaign for Trump in the next general election cycle.
"I don't get confused", Haley said in a sharply-worded rejoinder to the West Wing.
Haley, 46, was the senior most Indian-American official in the Trump administration.
But she said in her resignation letter to Trump she would "surely not be a candidate for any office in 2020" and would support his re-election bid.
Powell, who was born in Egypt and immigrated with her family to the United States, was deeply involved with working to improve the administration's relationships with allies in the Middle East and elsewhere. We passed the toughest sanctions against any country in a generation, pressuring North Korea toward denuclearization. She had scripted history by becoming the first-ever Indian-American to be appointed to a cabinet-level post in any U.S. administration.