Speaking after meeting Lebanese leaders, French foreign minister says there had been "a lot of progress" over the French proposals
The setback, barely a month before the Masters, inevitably raises concerns about whether he will be physically ready to defend his title at Augusta National.
"It was not an easy decision," Woods said in a Twitter post of skipping the Players.
"I have to listen to my body and properly rest when needed. My back is simply just not ready for play next week. I'm sad to miss one of the best events of the season, OUR Championship."
Former world number one Woods has not competed since the Genesis Invitational at Riviera in mid-February, where he finished last among those who made the cut and complained of back stiffness.
Woods then skipped the WGC-Mexico Championship, Honda Classic and this week's Arnold Palmer Invitational.
A source with knowledge of the matter told Reuters that Woods tweaked his back while testing drivers before the Genesis, where he serves as tournament host.
"He's still sore from that. He probably shouldn't have played Riviera," the source said, speaking on the condition of anonymity.
The Players Championship, the PGA Tour's flagship event, starts next Thursday at TPC Sawgrass in Ponte Vedra Beach.
Woods, a two-time winner of the event, carded a three-under-par 69 in the final round last year en route to a share of 30th place before going on to capture his 15th major title four weeks later at the Masters.
The 44-year-old Woods has been shortening his schedule in recent years while battling numerous injuries but is now running out of options to get competitive rounds in ahead of the April 9-12 Masters.
Woods does not play the week before a major, which leaves the March 19-22 Valspar Championship and following week's WGC-Dell Technologies Match Play as the only viable options before the year's first major.
He has played just twice this year, and it would hardly surprise if Woods heads to the Masters without playing any lead-up event.
He has had multiple back surgeries, including a fusion of his lower spine in 2017 that gave him a new lease on life and allowed him to resurrect a career that was in danger of petering out amid searing back and leg pain.
Woods looked to be swinging freely when he won the Zozo Championship in Japan in October, matching Sam Snead's record 82 PGA Tour victories, and he was arguably the best player on either team at the Presidents Cup in Australia in December.
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