Former Vice President Joseph R. Biden Jr. endorsed a national assault-weapons buyback program for the first time on Monday night, joining other Democratic presidential candidates in calling for new gun control measures in the wake of two mass shootings over the weekend that left 31 people dead.

In an interview on CNN, Mr. Biden also reaffirmed his support for universal background checks on new gun purchasers and for a ban on assault rifles. And on Tuesday morning, Mayor Pete Buttigieg of South Bend, Ind., released his own plan aimed at curbing gun violence and extremism, becoming the latest candidate to propose a nationwide gun licensing system.

As the nation reels from the shootings in El Paso and Dayton, Ohio, many of the 2020 contenders are eager to explain what they would do about gun violence if elected president. While the field of two dozen hopefuls has largely agreed on a set of ideas that Democrats have been trying to advance unsuccessfully for decades, some candidates have latched onto more progressive policies that previously might not have been politically palatable.