* Bond yields rise as European stocks hit highs
* Underlying uncertainty remains
* Record-breaking demand for Italian 15-year BTP deal
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Adds central banks, comment, Italian bond sale details)
LONDON, Feb 11 (Reuters) - Government bond yields across the euro area rose on Tuesday in response to gains by world stock markets, but did not venture too far from recent lows in a sign of underlying investor caution.
The death toll in mainland China from the coronavirus climbed past 1,000 on Tuesday, but the number of new confirmed cases fell.
The outbreak is hitting a peak in China this month and may be over by April, the government's senior medical adviser said on Tuesday.
World stocks resumed their rise towards record highs and the pan-European STOXX 600 index rose as much as 1% to a record high around 428 points.
Still, analysts said concerns that the coronavirus will hurt the world economy, alongside political uncertainty in Germany, prevented a deeper sell off in bond markets.
Indeed, in one sign of unease over the economic outlook, the spread between yields of three-month and 10-year U.S. Treasuries turned negative again on Monday.
And in the euro area, a key long-term measure of market inflation expectations - the five-year, five-year breakeven forward - fell below 1.23% on Tuesday to its lowest since early December.
"The story this morning is that the risk recovery in Asian markets is questioning the low yield levels we saw yesterday -- Bund yields at -0.40% are hard to defend when stocks are doing well," said Commerzbank rates strategist Christoph Rieger.
"Having said that, at these levels, EGBs (European government bonds) are very resilient given the lingering uncertainty, aided by uncertainty in Germany as well."
Annegret Kramp-Karrenbauer, the woman who had been expected to become Germany's next chancellor, said on Monday she would not run for the top job -- succumbing to a scandal involving the far right and blowing open the race to succeed Angela Merkel.
10-year bond yields across the bloc were up 2 basis points on the day in late trade.
Germany's benchmark Bund yield rose to -0.39% not far off a low of -0.41% hit on Monday.
It is down around 20 bps so far this year on concern that the coronavirus outbreak will hurt economic growth and encourage the European Central Bank to maintain an easy monetary policy stance.
The Bund fell from the day's high of -0.38% after Federal Reserve chairman Jerome Powell's semi-annual testimony to congress. He cited a potential threat from the coronavirus in China and concerns about the economy's long-term health while being upbeat on the general outlook for the U.S. economy.
But yields may also have edged away from highs on the back of an MNI news story suggesting the chances are rising of an ECB rate cut if eurozone economic data continues to disappoint and the coronavirus persists as a threat to global trade, according to DZ Bank rates strategist Daniel Lenz.
Elsewhere, Italy priced 9 billion euros of 15-year bonds via a syndicate of banks on the back of record demand exceeding 50 billion euros. (Reporting by Dhara Ranasinghe and Yoruk Bahceli; editing by Larry King and Alexandra Hudson)