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

AMSTERDAM, Sept 23 (Reuters) - Italy's 30-year government bond yield hit a record low and the benchmark 10-year yield neared an all-time low on Wednesday as the risk of a snap election there faded, while broader focus was on weak business activity readings.

Euro zone business growth ground to a halt this month, a survey showed on Wednesday, throwing the economic recovery into question and triggering expectations of fresh stimulus by governments and central banks.

"Today’s statistics constitute a very worrying signal for policymakers, both governments and the ECB, and an incentive to do more to support economic conditions," Christopher Dembik, head of macro analysis at Saxo Bank said.

Matteo Salvini's far-right League failed to deal a fatal blow to Italy's coalition government in regional elections held on Sunday and Monday, and voters approved a referendum cutting the number of seats in parliament, both making a snap election less likely.

Italian bond yields tumbled on Tuesday and on Wednesday the 30-year yield dropped to as little as 1.755% in early trade .

Ten-year yields fell to their lowest since early October last year at 0.83%. Bond yields were down 1 to 2 basis points across Italy's curve.

On the Tradeweb platform 10-year yield fell to 0.768% less than one basis point from its all-time low hit in September 2019 at 0.761%.

"With the odds for snap elections also remote after recent votes, investors should thus remain comfortable to capture carry in BTPs," Commerzbank analysts told clients, referring to a trade where investors use cheap funds to invest in higher-yielding assets like Italian bonds.

Data offered marginal support to safe-haven government bonds, with Germany's 10-year yield last down about 1 basis point to -0.51%, below the -0.539% hit on Monday when concern around the rising number of European coronavirus cases mounted.

The growth and inflation outlook in the euro zone has not deteriorated since the European Central Bank's latest decision, board member Yves Mersch said.

He noted that extending the flexibility of the pandemic bond purchases to the ECB's conventional bond buying, as a Financial Times story suggested on Sunday, could risk legal scrutiny.

That was in contrast with recent dovish statements from other ECB policymakers, which have led investors to ramp up their bets for rate cuts in 2021.

Germany's cabinet approved a draft 2021 budget which envisages net new debt of 96.2 billion euros, the second-highest amount since the end of World War Two.

(Reporting by Yoruk Bahceli; Additional reporting by Stefano Rebaudo; Editing by Hugh Lawson)