Senate Republicans included $1.6 billion for the first installment of President Trump’s border wall in the new homeland security spending bill they released Tuesday, keeping the president’s marquee immigration promise on track.

While avoiding the term “wall,” the Senate bill calls for $1.6 billion in funding for “physical barriers” and border roads — matching Mr. Trump’s original request for money to build or repair fencing along 74 more miles of the U.S.-Mexico line.

The homeland security measure is one of a series of spending bills the GOP released Tuesday as they geared up for an end-of-year battle over 2018 funding.

“This legislation will help enhance border security, provide relief from natural disasters, and help adapt to evolving threats against our country,” said Sen. John Boozman, Arkansas Republican and chairman of the subcommittee that oversees homeland security money.

Mr. Trump had requested money to build new fencing in one part of Texas, to erect new levee wall along the Rio Grande in another part of Texas, and then to repair old fencing in San Diego.

The House has already passed a security-spending bill with the money included.

But Sen. Patrick Leahy, Vermont Democrat and vice chairman of the Appropriations Committee, called inclusion of the wall money a mistake.

“This is bumper sticker budgeting to save face for one of President Trump’s failed campaign promises,” he said.

He said the money could have gone to education, food assistance for the poor, new infrastructure or other needs he said were more pressing.

Mr. Leahy also blasted the process Republicans used, saying that if they’d actually put the bills through committee he would have had a chance to offer an amendment delaying wall construction until Mexico agreed to pay for it — as Mr. Trump had repeatedly promised during the campaign.

The president still insists Mexico will foot the bill, but he has not officially proposed any methods to make that happen, and Mexico is adamant that it won’t pay.

Putting the money in bills that will go directly to the Senate floor also likely leaves senators with a take-it-or-leave-it decision, which could give even some anti-wall Republicans protection to vote for the broader spending bill that includes the wall money.

Eight prototypes for new wall designs have been built and are being tested along the border in San Diego, but it’s unclear what role they’ll play in future construction. Customs and Border Protection officials have said the designs are intended to learn from.

The administration has also been reluctant to provide a vision for the wall, saying instead that it will make requests each year based on the most urgent needs Border Patrol agents identify.

That’s frustrated both Republicans and Democrats on Capitol Hill, who say before money is shelled out Mr. Trump should say how much fencing he eventually wants to build, and where.