A statement released yesterday says Khalid Masood taught English in Saudi Arabia from November 2005 to November 2006 and again from April 2008 to April 2009.
The embassy says he had a work visa. It says he returned for six days in March 2015.
The embassy says he wasn't tracked by Saudi security services and didn't have a criminal record there.
Before taking the name Masood, he was known as Adrian Elms. He was known for having a violent temper in England and had criminal convictions.