Senate Republicans on Tuesday laid down their ante in the new border wall spending battle with a homeland security spending bill that includes $5 billion in additional money to build more fencing in 2020 and fulfill President Trump’s top campaign promise.

The bill advanced through a spending subcommittee with some bipartisan support, but not before both Republicans and Democrats warned Mr. Trump against a repeat of his move earlier this year to grab money from the military and shift it to wall-building.

Tuesday’s action was a small step.

The $5 billion, if it survives the rest of the legislative process, would bring total wall funding under Mr. Trump to $14.8 billion. But Senate Republicans will have to battle with House Democrats, who included no border wall money in their version of the homeland security bill.

“This is a lot of damn money. I mean, it’s a lot of money,” said Sen. Jon Tester, a Montana Democrat who said he will not be able to support the legislation because of the wall money.

He complained that he didn’t have any clue how the $5 billion would be spent, and he asserted that Homeland Security Department officials don’t know either.

Sen. Shelley Moore Capito, the Republican chair of the subcommittee, disputed that. She said Homeland Security presented a lengthy justification for its border wall plans last year, delivering a thick volume of plans and an extensive briefing on how the money would be used.

“With the $5 billion that’s in this bill, this gets us through the top 17 in the high-priority areas,” Ms. Capitol said.

The $5 billion matches what Mr. Trump requested in his 2020 budget submission earlier this year.

He made the same request last year, but Congress ended up approving just $1.375. Mr. Trump then turned around and declared a border emergency and grabbed billions of dollars in Pentagon money he directed toward wall-building.

That move continues to irk senators in both parties.

“There is a line here that I believe has been overstepped,” said Sen. Lisa Murkowski, Alaska Republican.

She said she will back the $5 billion in this bill, but said she’ll vote later this week to end Mr. Trump’s latest emergency declaration earlier this month that redirected an additional $3.6 billion in Pentagon money to wall building.

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