* Italy yields fall to multi-month lows, German yields rise
* Budget optimism boosts Italian bonds
* China-U.S. trade tensions rise
* Germany sells 3.1 bln euros of 2-year bonds (Adds milestones, quotes, chart)
By Virginia Furness and Dhara Ranasinghe
LONDON, Sept 18 (Reuters) - Italy's government bond yields fell sharply on Tuesday on growing optimism that the new coalition's budget will respect European Union rules on fiscal discipline.
Two and five-year yields fell as much as 15 basis points to their lowest levels since July, while yields on short-dated top-rated German debt rose to four-month highs.
Italy's top ministers met on Monday to discuss the 2019 budget, with friction building inside the coalition.
Deputy prime ministers Luigi Di Maio and Matteo Salvini are pushing for a larger deficit than Economy Minister Giovanni Tria wants.
Although the news flow has made for choppy trade, analysts said Italian bonds continued to draw comfort from hopes that the talks will produce a market-friendly result.
A source told Reuters on Monday that Di Maio and Salvini sought a deficit of 2.0 to 2.5 percent to help pay for some of their main electoral promises, including the introduction of a "universal wage" for the unemployed and pension reform.
The news pushed Italian yields up to three basis points higher at the open but that move proved short-lived. Media also reported on Monday that the economy minister was set on preventing the 2019 budget deficit rising above 1.6 percent of domestic output, boosting Italian bonds.
Ten-year yields fell 11 bps to 2.76 percent, squeezing the gap over German Bund yields to around 227 bps -- the tightest in a week.
"Generally, the worries about the budget are dissipating," said Nordea Chief Analyst Jan von Gerich. "The big picture remains that some of the Italian risks are being priced out."
Analysts said it was encouraging that the latest headlines had not prompted a larger sell-off, particularly following a La Stampa report that quoted Di Maio as saying Tria could "go home". Di Maio said on Tuesday he did not ask for Tria's resignation.
Scott Thiel, BlackRock's deputy chief investment officer for fixed income, said on Tuesday he had recently moved to a long position in Italian bonds.
The renewed appetite for Italian risk was reflected in the ongoing sale of bonds from government agency Cassa Depositi e Prestiti (CDP) which had received bids of around one billion euros for a 500-million euro deal, its first since political turmoil erupted in the country this year.
Morgan Stanley analysts also noted that Italian bonds were attractive to foreign investors, especially those from Japan who could reap high returns on a currency-hedged basis.
They added that buying of Italian bonds by Japanese investors was contributing to a tightening of bond spreads, reducing the risk premium for euro zone assets and potentially pushing rates on core bonds higher.
Indeed, as Italian bonds yields fell, top-rated German bond yields rose.
Germany's 10-year Bund yield rose to its highest in almost seven weeks at 0.48 percent, while its short-dated yields hit four-month highs at minus 0.52 percent.
That move came as world trade tensions ratcheted up and stocks fell - developments that in recent weeks have benefited safe-haven German bonds.
Yields across other core bond markets also rose, , while U.S. 10-year yields climbed back above 3 percent.
(Reporting by Virginia Furness and Dhara Ranasinghe, additional reporting by Sujata Rao; Editing by William Maclean and Ed Osmond)