They also blasted Republicans on Capitol Hill and on the campaign trail for threatening to block a replacement until after the election.
Speaking at a Democratic dinner in Denver, both Democratic candidates offered their condolences to family members and friends of Scalia, but then quickly turned to politics.
"It appears that some of my Republican colleagues in the Senate have a very interesting view of the Constitution of the United States,” Sanders said. "Apparently they believe that the Constitution does not allow a Democratic president to bring forth a nominee to replace Justice Scalia. I strongly disagree with that.”
Clinton, too, argued Republican lawmakers who want to hold off on an appointment are meddling with the Constitution, calling their efforts “outrageous,” "disappointing,” and “totally out of step with our history and constitutional process.”
“Let me just make on point,” Clinton said, "Barack Obama is the president of the United States until January 20, 2017.”
Earlier in the day, following the passing of Scalia, Senate Majority Leader Mitch McConnell said he believed the vacancy should not be filled until after the election, and many other Republicans echoed the thought.
On the campaign trail, both Democratic candidates have talked about the importance of judicial appointments for the next president, and Clinton noted Saturday the longest it ever took to fill an Supreme Court vacancy was 100 days for Clarence Thomas.
"There are 340 days until the next president takes office," Clinton noted about Obama's remaining term. "So, that is plenty of time."