Several lawmakers Sunday called for reintroducing a ban on assault weapons in the wake of Friday's deadly school rampage. President Barack Obama is also likely to propose gun-policy changes, according to two administration officials.

Mr. Obama, on Sunday evening in Newtown, Conn., said that the nation as a whole is failing in its duty to protect its children and that "we will have to change," without specifying what changes are needed. He said that no law can prevent all violence,...