Democrats in the US House of Representatives have approved $4.5bn (£3.5bn) in humanitarian aid for the southern border.
Several migrant deaths, coupled with reports of "severely neglected" children at a Texan border patrol station, have helped shape the debate.
But the bill faces a tough path through the Republican-controlled Senate.
It is considering a rival bill with fewer restrictions on how border agencies can spend the money.
The Democrats' version, in contrast, contains several strict rules set out that the funds can be used for humanitarian aid only, and "not for immigration raids, not detention beds, not a border wall", a statement from House appropriations committee chair Nita Lowey said.
The White House said President Trump would be advised to veto the House bill if it landed on his desk "in its current form".
The administration accused the Democrats of seeking to "take advantage of the current crisis".