Democrats controlling the chamber are trying to dislodge the legislation from a Senate logjam over aid to hurricane-slammed Puerto Rico.
Friday's measure passed by a 257-150 vote over the opposition of most Republicans, who said it should include the Trump administration's $4.5 billion request for humanitarian aid and border enforcement. President Donald Trump took to Twitter on Thursday to urge Republicans to vote against the bill.
The House had passed an earlier $14 billion version of the measure in January, but the legislation has been held up in the Senate amid a fight between Trump and Democrats over aid to Puerto Rico.