Rajoy met with the head of the regional government of the Canary Islands, Fernando Clavijo, who also heads the tiny Coalicion Canaria party, a Popular Party (PP) spokesman said.
The party is one of the formations whose support Rajoy is seeking to back his bid to form a new government and end months of political paralysis which triggered a second general election on Sunday after inconclusive December polls.
The Popular Party won 137 seats in last weekend's vote - the most of any party and 14 more than in December but still not enough for an absolute majority in the 350-seat assembly.
To form a government the PP needs the backing of either its longtime Socialist opponents, who came second in the poll, or that of fourth-placed business friendly party Ciudadanos and several smaller groups.
At the very least, Rajoy would need the other parties to agree to abstain in a confidence vote to allow a minority PP government to function.
Rajoy has headed a caretaker government with limited powers since the general election on December 20 which resulted in a hung parliament, after which parties failed to agree on a coalition, prompting the repeat vote.