Barack Obama promises a second term marked by peace and equality for society, during his inauguration as president of the United States.

President Barack Obama opened his speech by declaring that a decade of war had ended, the nation’s economy is recovering and “America’s possibilities are limitless”. However the overall mood was more serious and thoughtful, emphasising the importance of the welfare state and his commitment to equality.

A flag-waving crowd of hundreds of thousands gathered in front of the White House as the president gave his inauguration day address.

It was a political speech that made reference to polarised battles between Republicans and Democrats, and in which the president pledged to address climate change and ensure a more equal society.

“We must make the hard choices to reduce the cost of health care and the size of our deficit,” he said. “But we reject the belief that America must choose between caring for the generation that built this country and investing in the generation that will build its future.”

The president also put forward a strong case for peace, saying that lessons had been learned from war, and that a powerful nation is marked by its capacity to be an “anchor of strong alliances”.

While he was officially sworn in on Sunday, as required by law, the celebration of inauguration day – including the parade down Pennsylvania Avenue and the night of balls – was reserved for Monday.

In a generally sombre address, intended to match the economic mood of the country, one of the biggest cheers was raised for President Obama’s commitment to gay equality: “Our journey is not complete until our gay brothers and sisters are treated like anyone else under the law.”

And he also put forward his vision for a more equal society overall, making a reference to immigrants, and and put his weight behind better welfare, saying: “For we, the people, understand that our country cannot succeed when a shrinking few do very well and a growing many barely make it.”

In a move that will excite environmental campaigners, a large passage of the president’s speech was reserved for climate change and a promise to respond to its threat: “Some may still deny the overwhelming judgment of science, but none can avoid the devastating impact of raging fires, and crippling drought, and more powerful storms.

There were fewer people and less excitement that when the president stood on the world stage four years ago, when a crowd of 1.8 million packed into central Washington knowing they were witnessing history.

As he enters his second term, Americans increasingly see Obama as a strong leader, someone who stands up for his beliefs and is able to get things done, according to a survey by the Pew research center for the people and the press.

The survey shows him with a 52 per cent job approval rating, among the highest rankings since early in his presidency. His personal favourability, 59 per cent, has rebounded from a low of 50 per cent in the 2012 campaign against Republican Mitt Romney.