Donald Trump maintained his huge lead in the crucial early voting state of Iowa in a major new poll by NBC News and the Des Moines Register but Nikki Haley is now emerging as his closest challenger. The former US president has a 27-point lead in Iowa three months before the first vote of the Republican primary as he attracted 43% support. But Haley, the former South Carolina governor and United Nations ambassador, climbed 10 points to 16%, sharing second place with Ron DeSantis, the Florida governor whose campaign has long been seen to be stalling. No other candidate scored significantly, even after second choices of supporters of Mike Pence, the former vice-president who suspended his campaign, were reapportioned. J Ann Selzer, the Iowa pollster who conducted the survey, said: “This is a good poll for Donald Trump. For all the things that happened between the last poll and now, he’s still the dominant player in the field and his standing has, in fact, improved from August.” Trump’s memory apparently hasn’t improved, though. In Sioux City on Sunday, he told supporters: “Well, thank you very much. And a very big hello to a place where we’ve done very well: Sioux Falls. Thank you very much, Sioux Falls.” A state senator, Brad Zaun, whispered: “It’s Sioux City, not Sioux Falls.” Trump said: “Oh … is that right?” To the crowd, he said: “So Sioux City, let me ask you: how many people come from Sioux City?” Trump is 77 but polling shows fewer Americans think he is too old for a second term than think so about Joe Biden, the president who turns 81 next month. Trump has made Biden’s age an anvil for his campaign to hammer but both men are closely watched for errors. In Sioux City, bragging about his relationships with authoritarian world leaders, Trump said Hungary “fronts on both Ukraine and Russia”. Hungary does not have a border with Russia. Haley has made foreign policy smarts part of her pitch to voters, strong debate performances also helping her rise. In the NBC/Register poll, she climbed 10 points from the same survey in August as DeSantis fell by three. Other candidates fell (the South Carolina senator Tim Scott from 9% to 7%, the former New Jersey governor Chris Christie from 5% to 4%) or stagnated (the entrepreneur Vivek Ramaswamy sticking at 4%). Haley was the second choice of 17% of likely caucus-goers, with 22% more saying they would consider her. Kristy Beckwith, 60 and from Ankeny, said: “I feel like she’s fresh, and I liked what she said about … the things that she did as governor of South Carolina … she’s a strong woman.” Trump faces 91 criminal charges, including for state and federal election subversion, and assorted civil trials. Nonetheless, he has increased his lead in the NBC/Register poll. In August, he led DeSantis by 23 points. He now leads by 27. Evangelical Christians remain a key Iowa voting bloc. Despite Trump facing criminal charges over hush-money payments to a porn star and a civil trial arising from a rape allegation a judge called “substantially true”, 65% of respondents to the NBC/Register poll said such legal problems would not stop him winning a general election. Trump enjoys bigger leads elsewhere. On Monday, the fivethirtyeight.com national polling average put Trump at 57%: 43% clear of DeSantis and 49% up on Haley.