President Obama on Monday began the first serious push of his administration to attempt to reduce gun violence, directing Cabinet members to formulate a set of proposals that could include reinstating a ban on assault rifles.

The effort will be led by Vice President Biden, according to two people outside the government who have spoken to senior administration officials since Friday, when a gunman killed his mother and rampaged through Sandy Hook Elementary School in Newtown, Conn., killing 20 children, six adults and himself.