WASHINGTON — Jill Biden and Defense Secretary Leon Panetta joined an effort Wednesday to build an education center at the Vietnam Veterans Memorial to tell the stories of generations of veterans killed in combat, including the wars in Iraq and Afghanistan.

They gathered with military families for a ceremonial groundbreaking on a site next to the Lincoln Memorial on the National Mall for the $85 million museum. Organizers still must raise $38 million before construction can begin.

The veterans group that built the Vietnam memorial wants to open the center in 2014, in time to welcome the last troops home from Afghanistan....