* Bond yields dip, market supported by ECB rate outlook
* Oil prices jump, German industrial orders fall
* Bund yield hits near 3-week low, Italian bonds outperform
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates prices, developments in Italy)
LONDON, May 7 (Reuters) - Euro zone government bond yields dipped on Monday as an unexpected fall in German industrial orders served as a reminder that a softening in economic data will encourage the European Central Bank to prolong an unwinding of stimulus.
The biggest yield falls came in Italy after the leader of Italy's far-right League, Matteo Salvini, raised the possibility that his electoral ally Silvio Berlusconi could "step aside" to allow a government to be formed after two months of deadlock.
Broader bond markets, while subdued by a holiday in London, were supported by the latest signs of weakness in the euro zone economy. Ten-year bond yields were down 1-3 basis points on the day .
German industrial orders unexpectedly dropped for the third month running in March due to weak foreign demand, data showed.
A growing perception that a rise in interest rates will come later than anticipated due to slowing growth momentum and subdued inflation has underpinned euro zone bond markets although a jump in oil prices could limit further falls.
"Bonds are a bit firmer on the back of the softer German data," said Commerzbank rates strategist Rainer Guntermann. "A lot has been repriced in terms of the ECB so the outlook for bonds is a bit more mixed."
U.S. oil prices rose above $70 a barrel on Monday for the first time since November 2014 on a deepening economic and social crisis in Venezuela and a looming decision on whether the United States will re-impose sanctions on Iran.
Still, Germany's 10-year bond yield dipped two bps to 0.52 percent, an almost three-week low.
Italy's 10-year bond yield fell three bps to 1.76 percent , extending falls after Salvini's comments.
Earlier on Monday Salvini said he had asked Italy's president to give him a mandate to try to form a government to end the deadlock.
5-Star says it is ready to form a government with the League but will not enter a coalition that includes Berlusconi. So far Salvini has refused to abandon his old ally and Berlusconi has rejected any suggestion that he should withdraw.
The Italian/German 10-year bond yield gap narrowed to 123 bps. On Friday it hit 126 bps, the widest in over two weeks.
"Italian BTP/Bund spreads will be further put to the test by last ditch efforts in Italy to hammer out a government coalition," said Benjamin Schroeder. (Reporting by Dhara Ranasinghe, Editing by Hugh Lawson, William Maclean)