* Italy, Spain debt yields fall on Greek buyback hopes
* Bunds edge lower but losses curbed by U.S. budget concerns
By Emelia Sithole-Matarise
LONDON, Dec 4 (Reuters) - Italian and Spanish bonds extended gains on Tuesday as relief that Greece could be on its way to clinch its next aid tranche underpinned demand for higher-yielding euro zone bonds.
The firmer tone in peripheral bonds kept German Bunds on the back foot, though losses were limited by signs U.S. lawmakers could be headed for an impasse over budget talks that could push the world's biggest economy into recession.
Italian 10-year yields fell 5 basis points to 4.40 percent while the Spanish equivalent was last 3 ticks down at 5.24 percent, extending Monday's falls after Greece unveiled better than expected terms for a debt buyback crucial for it to get bailout funds in coming weeks.
The buyback is part of a deal reached last week by Greece's international lenders to cut its debt pile and needs to be completed before the IMF can release its share of the aid.
The buyback terms improved the chances of its success, prompting investors to keep piling into lower-rated euro zone bonds and driving the Italian 10-year yield premiums over Bunds below 300 bps for the first time since March.
"We think that the big items such as an imminent bankruptcy in Greece is off the table. The overall climate is in favour of investors looking for yield everywhere and so the way of least resistance is for a narrowing of yield spreads," Piet Lammens, a strategist at KBC said.
With debt issuance petering out into the year end and Spain expected to eventually request aid that would trigger European Central Bank (ECB) buying, Lammens expected Spanish yields in particular to fall below 5 percent by the end of the year.
"People are underinvested with their cash and with Europe looking a lot more stable that makes a fundamental difference in terms of people's mind-sets," a trader said.
"To be underinvested in high-yielding periphery costs you money. So I see more and more momentum going into year-end for the risk rally to continue."
Greek bond prices were slightly lower in price after Monday's sharp rally with details of the bond buyback due at the end of the week.
German Bund futures were last 10 ticks down on the day at 142.41 while cash 10-year yields were up one bp at 1.42 percent.
Although Bunds remained under pressure, the more upbeat outlook for Greek aid, traders saw little scope for a sharp sell-off as concern over an impasse in U.S. budget talks propped up demand for highly liquid debt.
Investors were doubtful that U.S. lawmakers will reach a deal in time to avert recession-inducing fiscal tightening in the world's biggest economy early next year after the White House dismissed proposals by Republicans for steep spending cuts.
"The fiscal cliff debate rumbles on...the growth implications if they don't get something sorted out are fairly severe and as long as that remains in play, core markets remain reasonably well supported," a trader said. (Editing by Chris Pizzey, London MPG Desk, +44 (0)207 542-4441)