* US data shows modest jobs growth in Sept
* Euro zone bond yields steady, set for 3rd week of falls
* Euro zone periphery govt bond yields tmsnrt.rs/2ii2Bqr (Updates prices to close, adds chart, bullets)
By Olga Cotaga and Dhara Ranasinghe
LONDON, Oct 4 (Reuters) - Euro zone government bond yields were set to fall for a third week on Friday, steadying on the day as data showed U.S. jobs growth increased modestly in September.
The U.S. jobs numbers were in the spotlight after a string of weak data this week, including a plunge in manufacturing activity to a more than 10-year low in September and a sharp slowdown in services industry growth to levels last seen in 2016, which heightened investors' recession fears.
Friday's data showed nonfarm payrolls increased by 136,000 jobs last month. August data was revised to show 168,000 jobs created instead of the previously reported 130,000.
"The lower ISM (manufacturing and services) numbers led markets to fear an upcoming recession. We do not expect it for the next two quarters," said Florian Ielpo, head of macroeconomic research at Unigestion.
"The job report is a confirmation of that: not only the number of job creations is in line with the past 12 months and 3 years (about 140k) but also, in its composition."
Euro zone bond yields inched higher after the data, but the move was not big enough to reverse Thursday's sharp falls in yields, leaving the bond market little changed as the session ended.
Most 10-year bond yields in the currency bloc were largely steady on the day. Germany's 10-year bond yield was flat at -0.59%, above session lows but still on track for a third straight week of declines.
Bonds had rallied on Thursday, sending yields lower, after the United States said it would impose 10% tariffs on European-made Airbus planes and 25% duties on European products such as French wine, as punishment for illegal EU aircraft subsidies.
This has prompted the European Union to consider taking retaliatory measures, German Foreign Minister Heiko Maas said on Friday.
A euro zone bond rally had stalled earlier in the week - while U.S. Treasury yields tumbled - as concern grew that the European Central Bank had only limited room to boost growth and inflation. But dismal economic data in the United States revived fears of recession and pushed euro zone yields back down.
The steep decline in U.S. bond yields this week has left the gap between two-year U.S. and German yields at its tightest since late 2017 at around 210 basis points.
Revised data on Friday showing the Italian economy grew slightly more than previously reported in the first half of this year aided sentiment towards the euro zone.
Elsewhere, Italy was ready to issue its first new dollar bond in nearly a decade, sources told Reuters on Thursday. The sale may be announced as early as next week.
Credit rating agency DBRS is expected to review its positive-outlook rating for Portugal on Friday night, two days ahead of a parliamentary election in which Prime Minister Antonio Costa is expected to win a second term.
Reporting by Olga Cotaga and Dhara Ranasinghe; Editing by Catherine Evans, Mark Potter and Gareth Jones