* Spanish, Italian yields continue to fall
* Optimism on summit moves lingers
* But pause for Bunds suggests some worries
By Kirsten Donovan
LONDON, July 2 (Reuters) - Spanish and Italian government bond yields continued to fall on Monday after euro zone leaders last week surprised markets by agreeing measures to stabilise bond markets in an attempt to stem the debt crisis.
Under pressure from Spain and Italy, euro zone leaders agreed on Friday to let their rescue fund inject aid directly into stricken banks from next year and intervene on bond markets to support troubled members, moves that helped yields on the two countries' bonds ease.
But German government bonds paused for breath after Friday's sharp sell-off, reflecting some hesitation with markets hungry for details of the measures and questions over how far the limited funds available in the region's rescue funds could be stretched.
Ten-year Spanish yields were down 10 basis points at 6.24 percent and two-year yields were down 28 bps at 4.13 percent, leaving the yield curve over 60 basis points steeper since Thursday's close.
"The steepening is being led by the front end as default risk is priced out of the market so using this as a barometer of residual optimism from the summit, it suggests that the proposals do appear to have legs," Rabobank strategist Richard McGuire said.
Italian 10-year yields fell 12 basis points to 5.70 percent, while two-year yields dropped 29 basis points to 3.51 percent.
But both countries yields - or funding costs - remained high versus historical levels and a Spanish bond auction on Thursday will be the first test of market sentiment since the European Union summit last week, with the country expected to sell up to 2.5 billion euros of paper.
Trading volumes are likely to be thin ahead of Thursday's European Central Bank policy meeting and Friday's U.S. employment data, which is often a big market mover.
The ECB is expected to cut its main refinancing rate 25 basis points to 0.75 percent on Thursday, with expectations that the deposit rate it pays banks to park cash overnight may also be cut to zero.
"A rate cut will be welcome, but while a short-term boost to sentiment, this is not a game changer," Societe Generale economists said in a note.
"With credit channels still impaired, a rate cut unlikely to significantly improve funding conditions for banks or sovereigns in the periphery."
September Bund futures were 16 ticks higher at 141.06, with 10-year yields down a basis points at at 1.57 percent.
"They delivered more than expected last week and markets did the right thing on Friday, although it was very quiet," said a trader.
"But it wasn't a game changer, the periphery may stabilise heading into the ECB meeting but that's probably about the best you'll see."
Coupon and redemption payments from Germany totalling around 40 billion euros this week should help support core paper, along with the prospect of another 50 billion euros of cash inflows from France, Austria and the Netherlands next week.