* S&P downgrades Italy to A, three notches below Moody's
* Periphery wider; concerns over Greece's next aid tranche linger
* Bank funding strains intensifying
By Marius Zaharia
LONDON, Sep 20 (Reuters) - German Bunds firmed and Italian bonds briefly jumped on Tuesday after Standard & Poor's cut Italy's credit rating, in another sign that the euro zone debt crisis is getting worse.
There were also fears about Greece's ability to secure its next international aid tranche, while funding strains in interbank markets intensified, keeping the outlook of further Bund gains intact.
S&P cut Italy to A from A+, preceding any move by Moody's, which was expected to be the first major credit ratings agency to downgrade the country. S&P now rates the country 3 notches lower than Moody's current Aa2 and 2 notches lower than Fitch's AA-.
"It was clear to everybody that Italy's rating was under some sort of pressure. But Moody' at least concluded that they were not yet ready to downgrade Italy so the timing came a bit of a surprise and S&P has already been most aggressive on Italy," said Rainer Guntermann, strategist at Commerzbank.
"It is also a reminder that there will be pressure on the ratings of some other countries."
Bund futures FGBLc1 last traded 31 ticks up on the day at 137.74, having risen as high as 138.14. German 10-year yields fell 3.3 basis points to 1.770 percent, within a whisker of record lows at 1.681 percent.
Guntermann said fresh bad news may be needed to test record low yields during Tuesday's session, but that the general risk backdrop will be supportive for Bunds for "some time to come" and they could move in uncharted territory soon.
Italian BTP futures FBTPc1 were last 26 ticks down at 99.59 in very thin trade, having fallen as low as 98.50 earlier in the session. The Italian/German 10-year yield spread briefly reached 397 bps in the session, before falling back to 386 bps, up 7 bps on day.
One trader said the spread narrowing was caused by a few small bids for Italian paper in thin trade. Another trader said there was talk of the European Central Bank buying Italian and Spanish debt, although he had not seen the flows.
Italian 5-year credit default swaps rose 27 basis points to 515 bps, according to monitor Markit.
Concerns over French banks were also hitting the market. Three sources said the Bank of China has stopped foreign exchange forwards and swaps trading with some banks, including France's Societe Generale , Credit Agricole and BNP Paribas .
The 10-year French/German spread was a tad higher on the day at 83 bps, but outright yields were lower, with traders saying investors were still happy to buy French debt due to the country's triple-A status.
DOUBTS OVER GREECE
Greece promised as many austerity moves as necessary to get its next aid tranche in a telephone call with senior officials of the European Union and the International Monetary Fund, but the lenders warned implementation was key.
Talks will resume on Tuesday and traders said they were still wary on Greece, which has a poor reform record and is off track with its fiscal targets.
"Talks seem to be going well in Greece, but I'm not convinced," a third trader said.
Market participants were also looking for a fresh easing of monetary policy from this week's Federal Reserve meeting that could hint at more coordinated action to address a gloomy economic outlook.
Fixed income markets were pricing in a move to extend the maturity of the Fed's Treasury assets, but a bolder move may boost risky assets and hit Bunds. (Reporting by Marius Zaharia; editing by Anna Willard)