She paused at times, her voice quavering.

“We’ll never know why people choose to do these painful things,” she said, “but sadly, we always find out how.”

Ms. Schumer said the package of plans “seeks to address the how,” vowing that these initial public remarks “will not be my last.”

Specifically, the senator is introducing legislation that would allow the Justice Department “to create rewards and penalties for states that submit or don’t submit all records into the background check system,” his office said, with a particular focus on the records of people with a history of mental illness and drug problems.

The Schumers also called on Congress to fully fund the Substance Abuse and Mental Health Services Administration, which the Senate has proposed cutting by $159 million, according to Mr. Schumer.

The event on Monday came about after a phone call from the senator to the comedian, who immediately expressed an interest in participating.

“I said, ‘Hi Amy, this is Cousin Chuck,’ ” Mr. Schumer recalled. “She said, ‘I hope you’re going to ask me to do something with you on gun control.’ ”

Ms. Schumer said she “had a lot of say” in the content of the announcement, adding, “I’m pretty stubborn.”