Edan Alexander's family describes his "battle between hope and despair" leading up to release

For the first time since the release Monday from Gaza of American-Israeli hostage Edan Alexander's by the militant group Hamas, his family spoke publicly about what their emotional reunion was like, and what their son went through.

In a news conference Tuesday from the hospital in Tel Aviv where her son is recovering, Yael Alexander said the moment she embraced him "time stood still," adding, "My heartbeat returned in sync with his."

However, she also shared that during his more than 580 days in captivity, "Every minute was a battle between hope and despair."