(BBC) Hillary Clinton, the defeated presidential candidate, says US President-elect Donald Trump must be given a chance to lead.

Appearing in public for the first time since conceding defeat, the Democrat said she hoped Mr Trump would be a successful president for all Americans.

“We have seen that our nation is more deeply divided than we thought,” Mrs Clinton said.

Donald Trump will become the 45th US president after an astounding victory.

He will hold his first transition meeting with outgoing President Barack Obama at the White House on Thursday.

Mr Obama, who congratulated his successor in a phone call in the early hours of the morning, said it was “no secret” that he and Mr Trump had pretty significant differences.

“Ultimately we’re all on the same team,” he said, and people had to remember that “we are Americans first, patriots first, we all want what’s best for this country”.

Mr Obama was heartened by what he heard in Mr Trump’s remarks last night, he said.

Mrs Clinton also urged her supporters to respect the election result, saying the constitution enshrines the peaceful transition of power.

“I’m sorry that we did not win this election for the values we share and the vision we hold for our country,” Mrs Clinton told her supporters in her address in New York.

“We have still not shattered that highest and hardest glass ceiling. But some day, someone will,” Mrs Clinton said, referring to her failure to become the first female US president.

“To all the little girls watching… never doubt that you are valuable and powerful and deserving of every chance and opportunity in the world,” she said.

House Speaker Paul Ryan paid tribute to his fellow Republican, saying he had “turned politics on its head” and would lead a unified Republican government.

Mr Ryan, a lukewarm supporter of the president-elect, said that his party’s strong showing in elections to the Senate and House of Representatives was thanks in no small part to Mr Trump.

He referred repeatedly to Mr Trump’s running mate, Mike Pence, as “my good friend” and “a good man”.

From January the Republicans will control the presidency and both houses of Congress – defying pollsters’ predictions.

Mrs Clinton’s running mate Tim Kaine paid tribute to her as “a history maker” and said that it was “uniquely difficult” to be elected to federal office as a woman in the US.

He said it was “an amazing achievement” that she had won the popular vote.

While US media report that Mrs Clinton is ahead in the popular vote by less than 1%, in the US electoral college system which determines the presidency, what matters is winning individual states.

The last time the defeated candidate won more votes cast than the person elected president was in 2000, when Republican George Bush defeated Democrat Al Gore.

Mr Trump overturned pollsters’ predictions to win in key battleground states including Florida, Ohio and Pennsylvania.

He has said his immediate priorities are restoring the country’s infrastructure and doubling its economic growth.