* Core yields fall 2-3 bps in jittery session

* Yields show little reaction to FT story on ECB policy review

* Spanish bonds unmoved by downgrade to credit outlook

* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr

LONDON, Sept 21 (Reuters) - Euro zone bond yields fell on Monday, with the German 10-year yield hitting a six-week low, as rising cases of COVID-19 rattled investors and sent some looking for the safety of government debt.

The moves lower were contained, however, with last week's dovish forward guidance from central banks keeping yields stuck in narrow ranges and investors awaiting a clutch of economic data this week.

Investors are becoming more cautious about Europe amid a sharp uptick in new COVID-19 cases. Denmark, Greece and Spain have introduced new restrictions on activity and Britain is considering a second national lockdown.

The German 10-year yield fell more than 3 basis points to -0.534%, its lowest level since early August, while the 10-year French yield declined 4 bps to -0.265%.

Despite Monday's falls, core euro zone bond yields remain stuck in tight ranges as very accommodating monetary policy dominates trading.

The Financial Times, citing two European Central Bank governing council members, reported that the ECB had launched a review of its emergency bond purchase scheme introduced in response to the coronavirus crisis in March.

The review would consider how long the Pandemic Emergency Purchase Programme (PEPP) should continue and whether some of its extra flexibility should be transferred to the ECB's longer running asset-purchase schemes, the newspaper said.

Many analysts and investors expect more ECB stimulus regardless of any review and the story had little immediate impact on bond yields.

"We find this surprisingly early, but at least this makes our call for more ECB action in December more solid in our opinion," said Gilles Moec, AXA Group chief economist.

Spanish bond yields reversed an earlier rise with the 10-year yield broadly steady on the day at 0.247%.

Credit ratings agency S&P Global Ratings on Friday revised Spain's outlook to "negative" from "stable", citing concerns about its policy response to rising economic and fiscal challenges, but maintained its rating of Spain at 'A/A-1' and market reaction was marginal.

Italian yields, which fell to six-month lows last week, inched higher. The 10-year yield was up 1 bp at 0.981% after last week touching as low as 0.942%.

Attention will turn to the state of the euro zone economic recovery later this week, with flash purchasing manager index data for September due on Wednesday.

"The euro area PMIs this month will be of more heightened importance than usual for the market. Last month, the PMIs signalled some first signs of divergence occurring in the path of recovery between member states and between sectors of the economy," RBC strategists said in a note.

(Editing by Ed Osmond; Editing by Kirsten Donovan)