US President Donald Trump has said he is considering declaring a national emergency to get a wall built on the southern border of the US, after meeting with congressional leaders to discuss the Government shutdown.

Mr Trump and Democratic leaders failed to strike a deal in sometimes combative talks to end the partial shutdown of the US Government, as they fought over Mr Trump’s request for $US5 billion to fund his signature wall on the Mexican border.

Emerging after more than two hours of talks as the shutdown hits the two-week mark, Mr Trump told reporters he could use executive authority to build the border wall, but wanted to try to negotiate it with Congress.

“I can do it if I want. We can call a national emergency. I may do it.”

Mr Trump said he had designated a team that would meet over the weekend with politicians to resolve the standoff over his demand for a border wall.

About 800,000 federal workers have been affected by the December 22 closure of about one-quarter of the Federal Government, as Mr Trump withheld his support for new funding until he secures $US5 billion ($7.14 billion) to start building the wall along the US-Mexico border that he promised during his campaign.

Such a wall, he has argued, is needed to stem the flow of illegal immigrants and drugs over the southwestern border.

Senate Democratic leader Chuck Schumer, who was among those meeting with the President, said Mr Trump had told congressional leaders he would keep the Government closed “for a very long period of time”.

Senator Schumer said his party’s leaders “told the President we needed the Government open — he resisted”.

“In fact, he said he’d keep the Government closed for a very long period of time, months or even years,” Senator Schumer said.

The new Speaker of the House, Nancy Pelosi, called it a “lengthy and sometimes contentious” meeting.

“We cannot resolve this until we open up Government,” she said.

Before the meeting, Mr Trump sent a letter to Congress to try to gain their support for his wall, suggesting he was unlikely to budge on his funding demands.

“Walls work. That’s why rich, powerful and successful people build them around their homes,” Mr Trump wrote in his letter.

“All Americans deserve the same protection.”

But Ms Pelosi had sought to separate the issue of the wall and Government funding, and called on Mr Trump and his fellow Republicans in the Senate to reopen agencies as border talks continue.

“The wall and the Government shutdown really have nothing to do with each other,” said Ms Pelosi, who has rejected any funding for what she has called an “immoral” border wall.

Senate Majority Leader Mitch McConnell said that even though the new Congress had convened with the Democrats holding a majority in the House of Representative, “the basic steps that are needed to end this unfortunate standoff really haven’t changed at all”.

Trump ‘too successful to be impeached’

Earlier, Mr Trump responded to rumblings of a move by Democrats to impeach him, tweeting that he was too successful and popular to be impeached.

How do you impeach a president who has won perhaps the greatest election of all time, done nothing wrong (no Collusion with Russia, it was the Dems that Colluded), had the most successful first two years of any president, and is the most popular Republican in party history 93%?

— Donald J. Trump (@realDonaldTrump) January 4, 2019

“How do you impeach a president who … had the most successful first two years of any president, and is the most popular Republican in party history,” Mr Trump tweeted.

“They only want to impeach me because they know they can’t win in 2020, too much success!”

The President responded to calls for his impeachment a second time after Democratic congresswoman Rashida Tlaib riled up a supportive crowd by using a swear word to describe Mr Trump and predicting he would be removed from office, just hours after she took her seat in Congress.

Mr Trump launched back, saying: “You can’t impeach somebody doing a great job.”

He added Ms Tlaib had “dishonoured herself and dishonoured her family” with the remarks.

“I thought is was highly disrespectful to the United States of America,” the President said.

House Speaker Ms Pelosi has been cautious about whether her new Democratic majority would ever impeach Mr Trump, but at least two of her members are ready to move forward.

California Representative Brad Sherman and Texas Representative Al Green introduced articles of impeachment against Mr Trump on Thursday, the first day of the new Congress.

I believe that Obstruction of Justice is the clearest and most provable high crime and misdemeanor committed by Donald J. Trump. Read my analysis published in the Huffington Post here. https://t.co/x9ud1LcxtT

— Congressman Brad Sherman (@BradSherman) January 3, 2019

Mr Sherman and Mr Green pushed to impeach Mr Trump in 2017 and 2018 but the House blocked those resolutions twice, with the help of Democrats who said the effort was premature.

Ms Pelosi has not ruled out impeachment but has called it a “divisive activity” that needs support from both parties.

She and House Judiciary Committee Chairman Jerrold Nadler, have said they want to wait for the outcome of special counsel Robert Mueller’s investigation into Russia’s meddling in the 2016 election and contacts with the Mr Trump campaign before making a judgement.

-with wires

-ABC