Analysts said markets had already priced in the drop in euro zone price growth in November, with German government bond yields hitting their lowest in over three months on Thursday.
Euro zone core inflation for November, which is closely followed by the European Central Bank, fell to 1.1 percent, against expectations for a rise.
Consumer prices in the 19 countries sharing the euro rose by 2.0 percent year-on-year in November after a six-year high of 2.2 percent in October as food and energy price hikes eased, the data showed.
Sliding oil prices in the last few months are slowing price growth in some countries, although in the euro zone's largest economy energy prices have risen.
A fall in U.S. Treasury yields on Thursday had fuelled a rally in core euro zone government bonds, as investors bet the European Central Bank could be forced to keep interest rates at record lows for longer because of economic headwinds.
Federal Reserve Chairman Jerome Powell also gave comments that many investors saw as a sign the U.S. Fed's tightening cycle was drawing to a close.
"The reason the Bund is not rallying that much on the back of these figures is that it has already been priced in. The yield has already been dropping for a while now, heading towards the 30 basis point, where there should be some resistance," said Cyril Regnat, an fixed income strategist at Natixis.
"The market will now be waiting for the G20 this weekend and that could be a reason why bonds are stabilising."
The 10-year German government bond was down a basis point at 0.315, its lowest since August 21. The 5-year bond was also close to a three-month low at -0.268 percent .
Other core euro zone bond markets in France and Austria were little changed.
In Italy, yields largely held on to the strong gains notched up this week.
A report in the Il Messaggero daily said on Friday that Italy's Prime Minister Giuseppe Conte and Treasury Minister Giovanni Tria are working on a proposal to cut the 2019 deficit target to reach a deal with the European Union.
Italy 's government has been targeting a deficit of 2.4 percent of gross domestic product in 2019, putting it on a collision course with Brussels.
"It's encouraging that there are signs some members of the government are pushing for a 2 percent deficit target," said Antoine Bouvet at Mizuho, predicting a rally in Italian bonds into the year-end so long as there are no more adverse headlines.
The Italian 10-year bond yield rose 1.5 basis point to 3.215 , while the 5-year was unchanged at 2.330 percent. (Additional reporting by Abhinav Ramnarayan Editing by David Holmes and Peter Graff)
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