Top two leaders from both parties of each chamber invited to meeting on Wednesday after president said he is ‘ready’ to negotiate

Donald Trump has invited congressional leaders to a White House briefing on border security on Wednesday, amid a government shutdown and political impasse over immigration and federal funding.

Details of the meeting’s agenda and full list of participants were not immediately clear late on Tuesday, but the Guardian confirmed that the meeting is scheduled for Wednesday afternoon, according to a congressional source.

The top two leaders from both parties of each chamber have been invited, the source said.

The president had said earlier on Tuesday that he is “ready, willing and able” to negotiate an end to the partial government shutdown that stretched into its 11th day and a new calendar year on 1 January, but insists any agreement include funding for “a good old fashioned wall” on the US-Mexico border.

The political gridlock is therefore set to continue into the new session of Congress on Thursday and probably beyond, as Democrats refuse to agree to taxpayers’ money for a wall and intend to introduce their own legislation to reopen the government without such funding.

Undeterred, Trump continued to plead his case on Tuesday by tweeting at the Democratic leadership.

“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 said on Tuesday afternoon.

The Democrats are preparing to take control of the House of Representatives on Thursday, when Pelosi is expected to be confirmed as speaker, after significant party victories in the midterm elections. They will vote quickly on several bills to reopen the government, while Republicans insist they will not pass any such legislation in the Senate, which they still dominate, that the president will not sign.

Trump had seemed resigned on Tuesday morning to the continuing stalemate. He tweeted: “The Democrats, much as I suspected, have allocated no money for a new Wall.”

Donald J. Trump (@realDonaldTrump) 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 - and our Country must finally have a Strong and Secure Southern Border!

Trump had earlier told Fox News in a year-end TV interview that he was “ready to go” on any deal, despite there currently being no prospect of one.

“I spent Christmas in the White House, I spent New Year’s Eve in the White House,” he said. “I’m here, I’m ready to go, it’s important. A lot of people are looking to get their paycheck.”

Adding that the Democratic congressional leaders Chuck Schumer and Nancy Pelosi “can come over right now”.

Trump has not reached out to Schumer and Pelosi directly, however, and spent the festive period trying to blame the Democrats for the government shutdown. This despite a meeting in the Oval Office earlier in December where Trump, in a highly unusual move, told Schumer and Pelosi that he would be “proud” to take responsibility for shutting down the government over the funding row for the wall.

Government departments are already suffering from the hiatus in funding and on Wednesday, 19 Smithsonian museums and the national zoo in Washington will be closed because of the shutdown.

Republican leadership does not appear ready to split with its president over the contentious issue. The Senate majority leader, Mitch McConnell, is likely to be confronted on Thursday with legislation passed in the House to reopen the government. But late on Monday, his spokesman, Donald Stewart, said Senate Republicans would not pass any such legislation 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.

There have been multiple indications from the Democratic camp that they won’t negotiate before Thursday at the earliest, despite hints that Republicans might be prepared to discuss a wider deal on immigration.

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The legislation that they are likely to pass on Thursday will not be radically different from legislation that was ready to be passed by Congress on 21 December and go to the president’s desk for signing, but which failed amid chaos on Capitol Hill, prompting the shutdown.

“It would be the height of irresponsibility and political cynicism for Senate Republicans to now reject the same legislation they have already supported,” Pelosi and Schumer said in a joint statement late on Monday.

The Democrats earlier on Monday had unveiled details of the bills they plan to introduce on Thursday.

They will include one bill to fund the Department of Homeland Security at current levels through 8 February, with $1.3bn for border security, such as fencing and other services – but not a wall. Trump has demanded $5bn and insists the wall be included.

Facebook Twitter Pinterest Democrats have legislation to re-open the federal government, without border wall funding. Photograph: Win McNamee/Getty Images

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On Monday afternoon it emerged that some of the most famous national parks in the western US are closing partially because of problems such as overflowing public toilets and garbage facilities, vandalism to fragile areas and resulting dangers to human and wildlife safety.

The shutdown, which has forced furloughs of hundreds of thousands of federal government employees, has left many parks without most of their rangers.

Meanwhile the issue of a wall has become a political football at a time when the migration of people from Central and South America, fleeing destitution and violence and hoping to settle in the US, has created a humanitarian crisis at the US border amid a crackdown by the Trump administration.

Chaos has descended in recent weeks as a result of a militarization of the border on the US side, attacks on migrants, detention of families, unscheduled releases of families from detention onto the streets, and the recent deaths of two young children, and others, in US border custody, sparking calls from the United Nations for an independent inquiry.