The ruling conservative Popular Party, led by Rajoy, won the highest number of votes on Sunday but it only obtained 122 seats out of the 350-seat parliament, falling short of the 176 needed for a parliamentary majority.
French President Francois Hollande is on track to win a solid parliamentary majority after a first-round election that leaves him strengthened heading into a flurry of talks with euro zone leaders that could make or break the currency union.
Dominique Strauss-Kahn, once a favourite to be the next French president, came home on Sunday to an expected icy greeting from party allies after a legal odyssey in New York that reshaped France's political landscape.
G8 leaders all back French Finance Minister Christine Lagarde's bid to run the IMF, Foreign Minister Alain Juppe said on Sunday, as she attacked a call to probe her role in a 2008 legal case that may harm her chances.
Faced with a legal and media onslaught, Dominique Strauss-Kahn is pulling together a crack team of investigators, former spies and media advisers to fight back against charges he sexually assaulted a hotel chambermaid.