Senate Majority Leader Harry Reid acknowledged on Tuesday that there was not enough support for the ban in the Senate, meaning it would fail when gun control legislation comes to the floor of the chamber next month.
Biden, who has led President Barack Obama's push for tighter gun regulations, said he was undeterred.
"We are still pushing that it pass," Biden told NPR in an interview, according to its website.
"I believe that the vast majority of the American people agree with us, the vast majority of gun owners agree with us, that military-style assault weapons are — these are weapons of war. They don't belong in the street," he said.