The contest is widely seen as a two-way race between Susana Diaz, the president of the southern region of Andalusia, and former party leader Pedro Sanchez who was ousted in a rancorous internal rebellion.
Diaz, 42, is the establishment favourite and is seen as more amenable to striking deals with the government if she wins the primary while Sanchez, 45, promises a more adversarial approach.
Rajoy's minority Popular Party (PP) government has relied on the Spanish Socialist Workers' Party (PSOE), the main opposition party, to pass key measures in parliament since it was sworn in for a second term in October 2016.
"If Sanchez wins, I expect that within a year, a year- and-a-half at most, Rajoy will call early elections," added a former PSOE strategist.
Nearly 1,90,000 card-carrying members of the PSOE are eligible to vote in the leadership primary at 2,900 polling stations nationwide, with the results expected after 9:00 pm (1900 GMT).
At a polling station in Moncloa, west of Madrid, close to the party's main headquarters, a representative said that by noon, almost a quarter of the 260 people registered there had cast their ballots.
"We have an opportunity to unite. From tomorrow, we have to calm down and engage in national politics, forget petty squabbles, and convince people to vote for us."
Former economics professor Sanchez was forced to resign in October over his staunch refusal to allow Rajoy to form a minority government following two inconclusive national elections.
The architects of the messy rebellion argued it was best to let a conservative PP government through rather than go to the third elections in a year and risk losing even more votes.
He argues that the Socialists must move further to the left to have any hope of winning back voters who have drifted to new far-left party Podemos.
He has not ruled out submitting a no confidence motion in Rajoy if he wins the leadership race.
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