Hempstead (New York): Republican Donald Trump vowed on Tuesday to hit rival Democrat Hillary Clinton harder in the next US presidential debate after she put him on the defensive by accusing him of being racist, sexist and a tax dodger during their first matchup. Clinton blasted Trump again the day after a forceful performance in the first of three scheduled presidential debates ahead of the November 8 election. The New York real estate mogul, she said, "was making charges and claims that were demonstrably untrue, offering opinions that I think a lot of people would find offensive and off-putting." Trump, making his first run for public office, praised himself for not attacking Clinton about the marital infidelity of her husband, former president Bill Clinton, during the debate at Hofstra University but said in a Tuesday morning interview with Fox News that he may take up the attack line going forward. "I may hit her harder in certain ways," Trump said in a telephone interview with "Fox & Friends." Trump added that when Clinton criticised him for his treatment of women, he resisted. "I was going to hit her with her husband's women. And I decided I shouldn't do it because her daughter was in the room." Clinton brushed off Trump's vow, saying, "He can run his campaign however he chooses." Trump himself had a high-profile affair with Marla Maples, the woman who would be his second wife while he was still married to his first wife, Ivanka Trump. He eventually divorced Maples and married his third and current wife, Melania Trump. The television audience for debate looks set to approach 80-million viewer record for such events set in 1980, early Nielsen viewership data cited by US media suggested. Trump sought to deflect criticism of his debate performance, saying the debate moderator, Lester Holt of NBC News, asked him "very unfair questions" and that he was given a "very bad" microphone. Clinton, speaking to reporters on her campaign plane, said, "Anyone who complains about the microphone is not having a good night." There are two more debates scheduled, on October 9 in St. Louis and October 19 in Las Vegas. Clinton highlighted what she described as Trump's downbeat message. "He talks down America every chance he gets. He calls us names. He calls us a Third World country. He talks in such dire and dark terms. That's not who America is," Clinton said. She said that "the real point is about temperament and fitness and qualification to hold the hold the most important, hardest job in the world." Clinton was under pressure to perform well on Monday night after a recent bout with pneumonia and an erosion in recent weeks in her lead over Trump in opinion polls. One line of attack was Trump's past remarks about women, a message designed to resonate with women who are still undecided about their vote and who could be pivotal in deciding the White House election. Trump, a former reality TV star who eschewed a lot of debate practice, was assertive and focused early on, interrupting Clinton repeatedly. As the night wore on, he became testy and less disciplined in front of the crowd. A CNN/ORC snap poll said 62 per cent of respondents felt Clinton won and 27 per cent believed Trump was the winner. Trump complained on Tuesday that issues from Clinton's 2009-2013 tenure as secretary of state were not addressed on Monday night, including topics he has assailed her on such as her use of a private computer server for government emails, a deadly attack in Benghazi, Libya, and the Clinton Foundation charity. In signs that investors awarded the debate to Clinton, Asian shares recovered after an early bout of nerves while the Mexican peso jumped on Tuesday. US equity markets kicked off their session with a modest gain but the advance was restrained by weakness in energy stocks as oil prices fell 2.5 per cent. Clinton's chances in the election also improved in online betting markets. Clinton, the first woman to win the presidential nomination of a major US political party, seemed to pique Trump when she brought up during the debate how Trump has insulted women. She pointed to Alicia Machado, who won the 1996 Miss Universe title, saying Trump had repeatedly insulted her. "He loves beauty contests, supporting them and hanging around them," she said. Trump, former owner of the Miss Universe pageants, was asked on Tuesday morning about Clinton's comments. He defended his insults of the Venezuelan-born woman who is now a US citizen. "She was the winner and she gained a massive amount of weight," Trump said on Tuesday of Machado. "And it was a real problem. We had a real problem. Not only that - her attitude - and we had a real problem with her." Clinton, 68, relentlessly sought to raise questions about her opponent's temperament, business acumen and knowledge. Trump, 70, used much of his time to argue the former first lady and US senator had achieved little in public life and wanted to pursue policies begun by President Barack Obama that he said have failed to repair a shattered middle class, with jobs lost to outsourcing and excessive government regulation. Trump suggested her disavowal of a trade deal with Asian countries was insincere. Her handling of a nuclear deal with Iran and IS militancy were disasters, he argued. Trump said Clinton had spent her "entire adult life" fighting the IS, a group that has existed for less than a decade. In one of their more heated exchanges, Clinton accused Trump of promulgating a "racist lie" by suggesting Obama, the first African-American US president, was not born in the United States. The president, who was born in Hawaii, released a long-form birth certificate in 2011 to put the issue to rest. It was not until this month that Trump said publicly that he believed Obama was US-born. "He has really started his political activity based on this racist lie that our first black president was not an American citizen. There was absolutely no evidence for it. But he persisted. He persisted year after year," Clinton said. Trump repeated his false accusation that Clinton's failed 2008 presidential campaign against Obama started the so-called "birther" issue. Clinton suggested her opponent was refusing to release his tax returns to avoid showing Americans "he's paid nothing in federal taxes" or that "not as rich as he says he is." "It must be something really important, even terrible, that he's trying to hide," she said. Trump said that as a businessman, paying low taxes was important. "That makes me smart," Trump said.