The country has been without a fully-functioning government for eight months as squabbling political parties are unable to reach any kind of pact following in conclusive elections in December, and again in June.
Rajoy's conservative Popular Party (PP), which has led the government since 2011, won the greatest number of seats in both polls but fell short of a majority.
It has so far failed to secure support from other parties to form a minority or coalition government.
Rajoy will put his candidacy for another term to a first vote of confidence in parliament on Tuesday.
“The formation of a government in Spain is today still more of a wish than a fact,” he told a party rally in the northwestern region of Galicia, a PP stronghold, ahead of the vote.
The PP holds 137 seats, 39 short of a majority in the 350-seat parliament.
It has been in talks with its upstart centrist rival Ciudadanos which came fourth in the election with 32 seats but no final agreement has been struck.
Even if Ciudadanos agrees to support Rajoy's PP in the confidence vote, the two political groups will still fall short of the needed majority of seats.
Rajoy also needs the support of the Socialists, his traditional rivals, or at the very least their abstention when he asks for a confidence vote in parliament. So far they have refused to help him.
The Socialists finished second in the last election with 85 seats.
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