A poll on Thursday showed less than one third of Spaniards seek a re-run of last Sunday’s election, with two-thirds supporting a pact between parties.
About 87.1 percent of those surveyed said they would repeat their same vote, while just seven percent said they would change their vote in a fresh election.
On Sunday, centre-right Rajoy’s PP won Spain's general election with 123 seats, followed by the opposition Socialists with 90 seats - their worst result ever. However, the PP fell short of a majority and will need allies to get the 176 seats necessary for the 350 seat parliament if it is to govern the country for another four-year term.
Both PSOE and PP lost significant ground to the relatively new liberal Cuidadanos and anti-austerity Podemos parties.
According to the poll, only 1.4 percent of PP supporters want to change their vote in a new election while 6.8 percent of PSOE supporters were determined to vote for a different party.
Also, about 27 percent said they would want to see Rajoy remain as the prime minister, while 26 percent preferred Podemos leader Pablo Iglesias to become prime minister.
The poll was carried out on Monday and Tuesday by Invymark for the television channel La Sexta, in which about 1,200 people participated.