European shares fell in thin trade on Monday while the dollar held firm after U.S. Federal Reserve Chair Janet Yellen indicated that the central bank was poised to raise interest rates this year.

U.S. shares fell on Friday after Yellen suggested the Fed was ready to act if the economy kept improving as expected, though a raft of recent data has suggested it is growing only modestly in the second quarter. She said delaying a policy tightening until employment and inflation hit its targets risked overheating the economy.

A warning on Sunday by Greece's interior minister that the country will not be able to meet a June 5 repayment to the International Monetary Fund, and political concerns in Spain after the ruling People's Party took a battering in regional and local elections, also weighed on European shares.

The benchmark French CAC 40 .FCHI index fell 0.7 percent by 0940 GMT. Trading volumes were thin as several markets including Germany, the United Kingdom and the United States were shut for holidays.

Spain's IBEX IBEX was down 1.8 percent after voters in regional and local elections on Sunday punished Prime Minister Mariano Rajoy's ruling PP for four years of austerity while Greece's ATG share index .ATG fell 1.6 percent.

"The Greek debt warning and the Spanish election outcome are weighing on the markets, said Naeem Aslam, chief market analyst at AvaTrade.

In foreign exchange markets, the dollar firmed near a two-month high against the yen and held gains against the euro after Yellen's comments and as stronger-than-expected underlying U.S. inflation supported the Fed's case for an interest rate hike later this year.

Data on Friday showed the U.S. Labor Department's gauge on core consumer goods prices rose by 0.3 percent last month, bringing the year-on-year rise to 1.8 percent, the highest since October.

The dollar rose as high as 121.78 yen JPY=, jumping from a low of 120.64 on Friday, helped by a rise in Treasury yields US10YT=RR.

"I would expect rate expectations to continue to rise and for the dollar's uptrend to continue as a result," said Marshall Gittler, head of global FX strategy at IronFX Global.

The euro was down about 0.5 percent at $1.0964 EUR=, wallowing at its lowest levels since late April.

In the most explicit remarks so far about the likelihood of default if negotiations fail, Greece's interior minister said Athens cannot make debt repayments to the IMF next month unless it manages to reach a deal with its lenders.

Oil futures steadied after skidding ahead of the long U.S. holiday weekend, giving up about 2 percent on Friday as a rallying dollar and profit-taking took their toll.

Brent LCOc1 was down about 0.6 percent at $64.99 after dropping 2.1 percent for the week.

(Editing by Eric Meijer & Kim Coghill)