Senate Democrat, Chuck Schumer, said the Republican bill would be dead on arrival in the upper chamber, even if it passed the House.
In the US, the Council on American-Islamic Relations (CAIR) said it was "deply disturbed" by Biden's comments on the Gaza figures, and called on the president to apologize.
"One of the reasons Hamas moved on Israel ... they knew that I was about to sit down with the Saudis," Biden said at a campaign fundraiser.
In 2011, Israel swapped hundreds of Palestinian prisoners to win the release of one Israeli soldier, Gilad Shalit, who was held for five years.
United Nations Secretary-General Antonio Guterres said he was appalled by the attack but did not accuse either side.
The US president who just set a new standard of support for the Jewish state and the Jewish people in times of tragedy and war.
Protesters in Israel and the United States have convened as part of a week of scheduled protests.
Many members of the US Congress are older than President Biden. Are they still suitable?
One reported incident cited, First Lady Jill Biden could not hold the dog back from them.
The violent killing put a spotlight on the US civil rights cause after his mother, Mamie Till-Bradley, held an open-casket funeral and a photo of her son's badly disfigured body appeared in media.