The officials declined to discuss exact timing of the expected US air drop of aid into Gaza, although two officials said it could happen in the coming days.
This year's physical comes as Biden, a Democrat, and former Republican President Donald Trump, 77, prepare to face off in a likely rematch in the Nov. 5 presidential election.
Although there were still some "significant" gaps to close, the official said, adding, "It's pretty much there.”
The Republican-majority House passed an Israel-only bill in November, but it was never taken up in the Democratic-led Senate.