Hillary Clinton has told how the election result will be painful "for a long time", but urged her supporters to give Donald Trump an opportunity to be a great president with a peaceful transition to power. Holding back tears in a rousing speech to a room full of supporters, Ms Clinton urged Americans to never give up fighting for what they believed was right. Ms Clinton, flanked by her family, arrived at the New Yorker Hotel almost an hour after she was scheduled to speak after not appearing last night to publicly concede. "This loss hurts but please never stop believing that fighting for what's right is worth it," she said. She said the nation was more deeply divided than she thought. "But I believe in America ... and if you do then we must accept this result and then look to the future," Ms Clinton said. "Donald Trump is going to be our president. We owe him and open mind and the chance to lead. Our constitutional democracy enshrines the peaceful transition of power - and we don't just accept that, we cherish it." Ms Clinton then directly addressed young women who had been inspired by her candidacy. "Nothing has made my prouder than to be your champion ... never doubt that you are valuable and powerful and deserving of every chance and opportunity in the world to pursue and achieve your own dreams," she said. She said she was "sorry we did not win this election for the values we hold and the vision we share for our country". US President Barack Obama said he is now rooting for Donald Trump's success in uniting and leading the country. Mr Obama told how despite his well documented differences with Mr Trump he'd invited the President-elect to visit the White House tomorrow because he wanted to make his transition as smooth as possible. "The Presidency is bigger than any person," Mr Obama said. "We are now all rooting for his success in uniting and leading the country," he said. Mr Obama said he'd phoned Mr Trump at 3.30am local New York time last night after his victory became clear.He said he was "heartened" by Mr Trump's words about uniting the country. "Everybody is sad when their side loses an election but the day after we have to remember we're actually all on one team. We're not democrats first, republicans first - we're Americans first, we're patriots first," he said. He paid tribute to Hillary Clinton citing her "extraordinary life" of public service. Her Vice Presidential running mate Tim Kaine introduced Ms Clinton, saying he was "so proud" of her. Senator Kaine described her as a great history maker. He said in a nation that made it hard for a woman to be elected to office she had won the popular vote of Americans to be president. "That is an amazing accomplishment," he said. "She's held fast to dreams ... we know she would have made history as a president in one sense but we've never had a president who's made her whole career about families and children." Senator Kaine said she loved the country.