* European stocks hit session lows after poor U.S. PMI
* German flash manufacturing PMI shows lowest reading in 6-1/5 yrs
* Banks, auto stocks post steep falls (Updates to include U.S. PMI data, closing prices)
By Susan Mathew and Medha Singh
March 22 (Reuters) - European stock markets deepened losses on Friday, closing near session lows, as fears of a slowdown in global growth after weak manufacturing data from across Europe were exacerbated by dismal data from the United States.
After downbeat manufacturing activity from Germany reignited fears of a recession in the region's biggest economy, the inversion of the U.S. yield curve after similar U.S. data stoked fears that the world's largest economy may also be slipping into recession.
The pan-European STOXX 600 index, which had opened higher on relief at the extension of Britain's Brexit deadline, slipped for a third day to close down 1.2 percent to take weekly losses to 1.3 percent - its steepest this year.
The London and Paris bourses sank more than 2 percent, while Frankfurt and Madrid fared only slightly better with roughly 1.5 percent declines.
The euro zone-wide flash PMI also showed businesses performed much worse than expected this month, while French business activity slowed unexpectedly.
The classic gauge of fear – known as implied volatility, which tracks demand for options in European stocks – hit more than 9-week highs and posted its biggest weekly rise in a year, the first concrete sign of activity in a while.
Almost all sectors within the STOXX 600 were in the red with banks, auto and chemicals sectors down more than two percent each, along with industrial goods and services stocks. The bank sector posted its biggest daily drop sine early February.
Italian lenders Unicredit, Banco BPM, and UBI led losses among banks after Credit Suisse said the market is underestimating Italian banks' net interest income challenges.
Nestle, the world biggest food group, was the biggest drag on the benchmark, down 1.7 percent, followed by more than 2 percent dips in HSBC Holdings and oil and gas majors Total BP PLC.
"With numerous headwinds facing the manufacturing sector in Germany – including a slowdown in the automotive sector, Brexit, U.S.-China trade and a global economic slowdown – there's little to be optimistic about," said Craig Erlam, senior market analyst at Oanda in London.
Most European bourses had opened on a stronger footing, relieved at the European Union's agreement to at least a two-week reprieve that precludes Britain crashing out of the bloc without a deal next week.
Despite the relief from the summit overnight, there were more signs of firms making preparations for a no-deal Brexit, as British Prime Minister Theresa May now faces task of persuading a deeply divided parliament to back her Brexit deal. A no-deal exit could well have a depressive effect on Europe's major economies.
Goldman Sachs analysts reduced the likelihood of May's deal passing to just 50 percent, while raising the chances of "no-deal" to 15 percent. The bank continues to put the chances of no Brexit at all at 35 percent.
The odds of a no-deal exit had fallen to just 5 percent on online betting market Betfair. (Reporting by Medha Singh, Patrick Graham and Susan Mathew; Editing by Toby Chopra)