Donald Trump is convening a border security briefing on Wednesday for Democratic and Republican congressional leaders as a partial government shutdown over his demand for border wall funding entered its 12th day.

Mitt Romney: Trump's biggest failure is a lack of character in leading 'divided' nation Read more

The president “wants an agreement that reopens the government AND keeps Americans safe”, the White House said on Twitter. But so far, the administration has rejected a proposal from Democrats to reopen the government without money to build a wall along the US-Mexico border.

Ahead of the afternoon session, Trump met with cabinet secretaries in his first public appearance of the new year. The vice-president, Mike Pence, was expected to join as the shutdown drags into its second week, shuttering parks and leaving hundreds of thousands of federal employees without pay.

“Let’s make a deal?” Trump asked in a Tuesday tweet.

The partial government shutdown began on 22 December. Funding for the wall has been the sticking point in passing funding bills for several government departments.

Sign up for the new US morning briefing

The Wednesday afternoon briefing with the congressional leaders is taking place the day before Democrats are to assume control of the House and end the Republican monopoly on government.

The session will be held in the high-security Situation Room at the White House, which is typically used to handle sensitive information. The location means that the conversation will not be televised, unlike Trump’s volatile sit-down with Democratic leaders last month.

The exact agenda, however, was not immediately clear, according to a person with knowledge of the briefing who was not authorized to speak publicly about the issue and spoke to the Associated Press on condition of anonymity.

The Senate majority leader, Mitch McConnell, and the top incoming House Republicans – Kevin McCarthy of California and Steve Scalise of Louisiana – plan to attend, according to aides. The departing House speaker, Paul Ryan, is not expected.

The House Democratic leader, Nancy Pelosi, who is expected to become speaker on Thursday, and Senate Democratic leader, Chuck Schumer, plan to attend. Pelosi said on Tuesday that Democrats would take action to “end the Trump shutdown” by passing legislation on Thursday to reopen government.

“We are giving the Republicans the opportunity to take yes for an answer,” she wrote in a letter to colleagues. “Senate Republicans have already supported this legislation, and if they reject it now, they will be fully complicit in chaos and destruction of the president’s third shutdown of his term.”

The White House invitation came after House Democrats released their plan to reopen the government without approving money for a border wall – unveiling two bills to fund shuttered government agencies and put hundreds of thousands of federal workers back on the job. They planned to pass them as soon as the new Congress convenes on Thursday.

Responding to the Democratic plan, the White House press secretary, Sarah Sanders, late on Tuesday night called it a “non-starter” and said it would not reopen the government “because it fails to secure the border and puts the needs of other countries above the needs of our own citizens”.

Trump spent the weekend saying Democrats should return to Washington to negotiate, firing off Twitter taunts. After aides suggested there would not necessarily be a traditional wall as Trump had described since his presidential campaign, he insisted otherwise.

On Tuesday morning, after tweeting a New Year’s message to “EVERYONE INCLUDING THE HATERS AND THE FAKE NEWS MEDIA”, Trump tweeted: “The Democrats, much as I suspected, have allocated no money for a new Wall. So imaginative! The problem is, without a Wall there can be no real Border Security.”

But he seemed to shift tactics later in the day, appealing to Pelosi. “Border Security and the Wall ‘thing’ and Shutdown is not where Nancy Pelosi wanted to start her tenure as Speaker! Let’s make a deal?” he tweeted.

Donald J. Trump (@realDonaldTrump) Border Security and the Wall “thing” and Shutdown is not where Nancy Pelosi wanted to start her tenure as Speaker! Let’s make a deal?

Whether the Republican-led Senate would consider the Democratic funding bills – or if Trump would sign either into law – was unclear. McConnell’s spokesman, Donald Stewart, said Senate Republicans would not take action without Trump’s backing.

“It’s simple: the Senate is not going to send something to the president that he won’t sign,” Stewart said.

Even if only symbolic, the passage of the bills in the House would put fresh pressure on the president. At the same time, administration officials said Trump was in no rush for a resolution to the impasse, believing he has public opinion and his base on his side.

The Democratic package to end the shutdown would include one bill to temporarily fund the Department of Homeland Security at current levels – with $1.3bn for border security, far less than the $5bn Trump has said he wants for the wall – through 8 February as talks continued.

It would also include another measure to fund the departments of agriculture, interior, housing and urban development and others closed by the partial shutdown. It would provide money through the remainder of the fiscal year, to 30 September.