May 29 (Reuters) - Euro zone yields dropped in thin trade on Monday as investors bought bonds following a deal to raise the U.S. debt ceiling, but remained cautious ahead of the bloc's inflation data later this week.

T-bond futures were steady and the cost of insuring exposure to a U.S. debt default over the short-term was almost unchanged, while the Memorial Day holiday meant cash U.S. Treasuries were untraded.

The U.S. House Rules Committee said it will meet on Tuesday to discuss the debt ceiling bill, which needs to pass a narrowly divided Congress before June 5, when the U.S. Treasury says it would run short of money to cover all its obligations.

Germany's 10-year government bond yields, the bloc's benchmark, fell 11 basis points (bps) to 2.43%.

European stock indexes slipped slightly, lacking momentum while optimism over the U.S. having reached a debt ceiling deal over the weekend kept Wall Street futures positive.

Germany's two-year government bond yield, more sensitive to expectations for policy rates, was down 6 basis points (bps) at 2.92%.

On Friday, it hit its highest since March 15 at 2.991%, almost 30 bps below the close on March 9, the day before the banking turmoil started to affect financial markets.

Germany will publish consumer price data on Wednesday and euro area numbers will be released on Thursday.

"While we have the stronger conviction that the peak for (euro zone) core goods inflation is behind us, we now expect slower moderation from here," Ruben Segura-Cayuela, European economist at BofA, said in a research note.

"A strong summer season is likely to keep services inflation from clearly peaking in the next few months," he said, adding higher energy prices in the second half of the year meant "upside surprises can't be ruled out". He cited possible wage price rises and the risk of second-round effects.

BofA expects headline inflation to be 5.3% this year and 2.4% in 2024, with core inflation at 4.8% and 2.5%.

Irish central bank chief Gabriel Makhlouf said on Friday that more than two ECB rate hikes this year are possible given stubborn inflation.

Money markets have priced more than two rate hikes since early last week while postponing the peak in policy rates from September to December.

December 2023 ECB euro short-term rate forwards were at 3.72%, implying expectations for a deposit facility rate of 3.82% by year-end.

Spain's 10-year yield was down 11 bps at 3.49%, with the German-Spanish yield spread slightly widening to 105 bps.

Spanish Prime Minister Pedro Sanchez said the country would hold an early general election on July 23 after his Socialist Workers' Party (PSOE) lost ground in regional elections, while rival conservative People's Party and far-right party Vox outperformed.

Greece's 10-year yields dropped 1 bps to 3.87%, with the gap between Greek and German yields.

Greek bond prices jumped last week as the election outcome boosted expectations the country will continue its policies to support economic growth and cut debt.

Greece's president will appoint a caretaker prime minister on Wednesday to form a government to lead the country to a repeat election on June 25.

Markets believe a second vote that gives the leading party bonus seats will give the conservative New Democracy party the majority needed to rule alone.

(Reporting by Stefano Rebaudo, editing by William Maclean and Barbara Lewis)