Nancy Pelosi has made history once again after being sworn in as speaker of the House of Representatives and immediately issuing a warning to Donald Trump that Democrats may seek to impeach him.

On a day that was rich with symbols but not just symbolism, America elected a lower chamber of congress that was more diverse and contained more women than ever before. One of the first two Muslim women elected to congress, Rashida Tlaib was sworn in with her hand laid upon a centuries-old Quran that once belonged to Thomas Jefferson.

The new speaker, who first made history when she was elected to that job in 2007, was sworn in for the second time, saying that in November’s midterm elections the American people had “demanded a new dawn”.

“This House will be for the people,” said Ms Pelosi. “To lower health costs and prescription drugs prices, and protect people with pre-existing conditions; to increase paychecks by rebuilding America with green and modern infrastructure – from sea to shining sea.”

Facing his first day as president with a divided congress, Mr Trump appeared for a surprise news conference in the White House press briefing room hours after Mr Pelosi’s address to the House. He was quick to congratulate Ms Pelosi before pivoting to one of his favourite topics – border security and his oft-promised border wall with Mexico. The fight over funding for that wall has led to a partial government shutdown that has lasted two weeks.

“It’s a very very great achievement and hopefully we’re going to work together and get lots of things done, like infrastructure,” Mr Trump said of Ms Pelosi’s swearing in. “I think it’ll work out and be a little bit different than a lot of people are thinking.”

He then very quickly pivoted to the issue of border security and introduced several officials from the nation’s border control agency. He said of the press conference: “This was set up a long time ago. It just came at a very opportune time. We were in the Oval Office working on different plans.”

Yet, the remarks that perhaps captured most attention were delivered several hours earlier in an interview with NBC News, where Ms Pelosi declined to rule out the prospect of the president being impeached or indicted. She said it was possible special counsel Robert Mueller could seek an indictment against the sitting president, despite Justice Department guidelines against such action.

“I do not think that that is conclusive,” Ms Pelosi said of a memo that was written in 1973. “I think that that is an open discussion. I think that is an open discussion in terms of the law.”

Ms Pelosi’s swearing in was a personal victory for her, as well as the Democratic Party. Just two months ago there was talk of a leadership challenge to replace the 78-year-old.

As it was, in a display of political manoeuvring that underscored the Californian’s skills, she saw off any potential challengers before an individual was actually named to oppose her. On Thursday, she was elected speaker 220-192, with a dozen Democrats rejecting her. After taking the oath of office, she oversaw the swearing in of the new members of the US’s lower chamber.

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“Our common cause is to find and forge a way forward for our country. Let us stand for the people to promote liberty and justice for all as we pledge every day,” she said.

“And always, always keep our nation safe from threats old and new, from terrorism and cyberwarfare overseas and here at home to protect and defend.”

She said the House must also address climate change, which she termed “the existential threat of our time”.

Democrats have said one of their most pressing priorities will be to pass a funding measure to end the government shutdown.

The shutdown has come over Mr Trump’s demand for $5bn in funding for his border wall – one of his major campaign promises – as part of any spending bill to reopen the government.

Democrats have offered a fraction of that, for general border security, in legislation that will likely pass the House.

Yet, as vice president Mike Pence swore in newly elected senators, Senate Republicans under Mitch McConnell said they had no plans to consider the House bills to fund the government unless Mr Trump agreed to sign them into law.

“The wall – you can call it a barrier, you can call it whatever you want – but essentially we need protection in our country,” Mr Trump told reporters, without taking questions.

What Mr Trump cannot hold off is Democrats’ enthusiasm for holding hearings into his administration and calling members of his staff to testify. The chairs of three important committees have already said they intend to scrutinise the president’s actions in a way Republicans largely avoided.

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When it came to the Republicans turn to speak, minority leader Kevin McCarthy – who handed the gavel to Ms Pelosi in an act that underscored the shift in power – spoke about trying to avoid “retribution”.

“When we work together, we succeed together as one nation. We’re now entering a period of divided government, but that is no excuse for gridlock or inaction,” he said in comments that may not presage what takes place over the next two years in a toxic political environment.

As she gavelled the 116th congress into session, Mr Pelosi noted it was like no other that had proceeded it, and said it contained a “transformative freshman class”. Among its member are more Latinos, Native Americans and African-Americans than have previously served.

A sign of that diversity could be found on the Twitter feed of Ilhan Omar of Minnesota. Overnight, she tweeted a picture with her family at the airport. The House rules were being changed to allow her to wear a head scarf on the chamber floor, along with the other Muslim woman to join the chamber.