"We can't rest until all of our children can go to school or walk down the street free from the fear that they will be struck down by a stray bullet,'' Obama said in a keynote speech to the Congressional Black Caucus Foundation's annual awards dinner.
Legislation calling for expanded background checks failed to clear the Senate earlier this year despite a strong push by Obama, Vice President Joe Biden, people whose loved ones had been killed by gunfire and other gun-control advocates.
The bill was part of a package of measures Obama promised to put the full weight of his office behind after 20 first-graders and six educators were killed last December in a mass shooting at an elementary school in Newtown, Connecticut.
Republicans and some Democrats voted against the measure.
Obama used the occasion of his keynote speech to make his first public comments about this week's pair of shootings.
Just two days ago in his other hometown of Chicago, 13 people out watching a game of pickup basketball at a neighborhood park were wounded by gunfire, including a 3-year-old boy.
This past Monday in Washington, 12 people were slain by a gunman who later was killed by police. Obama was preparing to speak Sunday evening at a memorial service in Washington for victims of that shooting.
The White House said after Monday's shooting that Obama is using his executive authority to tighten access to guns and remains committed to strengthening gun laws, including requiring background checks for sales online and at gun shows.
The dinner celebrated the "Spirit of 1963,'' including the civil rights movement and the March on Washington for Jobs and Justice led 50 years ago at the Lincoln Memorial by Martin Luther King Jr.
The annual event also celebrated the advances the movement brought about for black Americans, including voting rights, desegregation and Obama's election in 2008 as America's first black president.
Without mentioning his place in history, Obama acknowledged progress made since 1963 but said there was more to be done. He spoke of work needed to reduce an unemployment rate among blacks that is twice that of whites, increase the minimum wage as he proposed earlier this year and provide health care and education for all.