* Bond yields rise as European stocks hit highs
* Underlying uncertainty remains
* Strong demand for Italian 15-year BTP deal
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates price action, news on Italy sale)
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 caution among investors.
The death toll in mainland China climbed past 1,000 on Tuesday, but the number of new confirmed cases fell. The government's top medical adviser on the outbreak, Zhong Nanshan, held out hope that the epidemic may peak in February and then plateau before easing.
World stocks resumed their rise towards record highs and the pan-European STOXX 600 index rose as much as 0.7% to a record high around 428 points.
Still, analysts said concerns that 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 1.24% 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.
Most 10-year bond yields were up 3 basis points on the day.
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.
ECB President Christine Lagarde is scheduled to speak later this session, while U.S. Federal Reserve Chairman Jerome Powell will deliver a semi-annual testimony to Congress.
The text of Powell's testimony was published on Friday, so focus was expected to fall on the question-and-answer session.
Elsewhere, Italy started selling a new 15-year bond via a syndicate of banks with orders for the new bond over 40 billion euros.
In mid-January, a 30-year BTP bond worth 7 billion euros ($7.63 billion) placed in a similar syndicated sale attracted record orders of around 45 billion euros, with 68% of the issue going to foreign investors. (Reporting by Dhara Ranasinghe, editing by Larry King and Alexandra Hudson)