WASHINGTON — House and Senate negotiators on Monday night agreed in principle to provide $1.375 billion for fencing and other physical barriers at the Mexican border, part of a broader agreement that would stave off another partial government shutdown without funding President Trump’s wall.

The agreement would allow for 55 miles of new bollard fencing, with some restrictions on location based on community and environmental concerns, according to two congressional aides, who requested anonymity to disclose details of the private negotiations. That is a fraction of the more than 200 miles of steel-and-concrete wall that Mr. Trump demanded — and 10 miles less than negotiators agreed on last summer, before Democrats took control of the House.

The deal, which must still pass the House and the Senate, and secure Mr. Trump’s signature, came together just before Mr. Trump, framed by banners emblazoned with “Finish the Wall” at an event in El Paso, doubled down on his demands.

“We’re building the wall anyway,” he told the crowd, saying that aides had told him that the negotiators had made progress.