In a series of articles published earlier this month, the paper took Bing to task over his comments questioning whether he was the father of Hurley's child, due in April. Hurley said at the time the comments made her "deeply distraught."
Almost immediately, The Mirror announced it was launching a hunt for Bing - whom it dubbed "Bing Laden" on a wanted poster-style front page - for "crimes against Ms. Elizabeth Hurley."
Several times the paper published Bing's Los Angeles-area office number and asked readers to call and "tell him exactly what you think of him."
Marty Singer, Bing's attorney, said his client received death threats as a result. The number has since been disconnected.
"This has gone beyond a simple defamatory article to where he feels his safety is at risk," Singer said. "I can't imagine an American publication doing this."
Officials with The Mirror could not be reached for comment. A recording said the building had been evacuated but did not explain why.
The suit, filed in Los Angeles County Superior Court in Santa Monica, asks for at least $10 million in compensatory and punitive damages. It also seeks to have the paper cease continued publication of the articles - something Singer said Bing had already formally requested it do.
Bing was also expected to send a letter to the British Press Complaints Commission requesting it review the case.
Bing released a statement Dec. 4 saying he and Hurley "were not in an exclusive relationship when she became pregnant."
© MMI The Associated Press. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed