WASHINGTON — The mother of a child killed in the school shooting in Newtown, Conn., delivered a raw plea on Saturday for the Senate to pass gun control legislation, using an avenue normally reserved for the president.

Struggling to maintain her composure, Francine Wheeler spoke of her 6-year-old son, Ben, who was killed on Dec. 14 at Sandy Hook Elementary School, as President Obama took the unusual step of letting someone else deliver the White House’s weekly address.“I’ve heard people say that the tidal wave of anguish our country felt on 12/14 has receded — but not for us,” Ms. Wheeler said with her husband, David, by her side. “To us, it feels as if it happened just yesterday. And in the four months since we lost our loved ones, thousands of other Americans have died at the end of a gun. Thousands of other families across the United States are also drowning in our grief.”

“Please help us do something before our tragedy becomes your tragedy,” she said.

The presence on Capitol Hill last week of the families of those killed in Newtown was considered a crucial element in getting the Senate to vote, 68 to 31, to proceed with debate on gun safety proposals. While the families of the 20 children and 6 educators killed do not all support tighter gun restrictions, those in favor of greater control have proved to be some of the most compelling advocates, successfully pushing for new laws in Connecticut.

Mr. Obama, after delivering his own appeal on gun control on Monday in Hartford, gave families a ride to Washington on Air Force One so they could lobby members of Congress. The president “believes their voices and resolve have been critical to the continued progress we’ve seen in the Senate,” Jay Carney, the press secretary, said of the families on Friday.