MADRID (Reuters) - A majority of voters of Spain's ruling conservative People's Party (PP) would consent to its leader and acting Prime Minister Mariano Rajoy stepping aside if this allowed the party to stay in government, a poll showed on Sunday.

Rajoy, blamed for harsh austerity measures implemented in recent years that crippled the economy as well as political corruption cases at the PP during his leadership, is seen as the main obstacle for other parties to back a PP government.

Spain returns to the ballot box on June 26 after an inconclusive December election stripped Rajoy's center-right party of its absolute majority. Opinions polls show the vote could produce another political stalemate, forcing PP to strike a 'grand coalition' deal with the Socialists and newcomer liberal party Ciudadanos to remain in power.

According to the Metroscopia poll in the daily newspaper El Pais, which questioned 1,200 people on June 7 and June 8, the vote still remains too fragmented for any clear government majority.

Among those polled, 57 percent of PP voters said they would accept Rajoy resigning his position if this meant securing a PP government, while 74 percent of overall voters thought Rajoy should go if this would pave the way for a new government.

An official survey released on Thursday showed voters are still not inclined to revert to the two-party system that dominated Spanish politics for the past 40 years. They seem likely to spread their votes among four main parties and four smaller ones.

While the PP would win the most votes, according to two separate polls published in El Pais and La Vanguardia on Sunday, it remains without a large enough presence in the lower house to take a second term alone.

The party led by Rajoy would win 29.8 percent of the vote, or between 119-122 seats in parliament, the GAD3 poll in La Vanguardia showed, far short of the 176 seats needed to win back its previous absolute majority.

Even if the PP were to rely on backing by natural allies, market-friendly Ciudadanos (Citizens), a resulting coalition would still fall short, holding just up to 163 seats, the survey showed.

Meanwhile, support for a joint left-wing group formed by Podemos (We can) and Izquierda Unidos (IU or United Left) would stay ahead of the Socialists, with the poll in La Vanguardia giving the group 85-87 seats in Parliament over the Socialists' 80-82.

The GAD3 poll questioned 1,016 people between June 6-9.

The Socialists again took a hit in both surveys, similar to two separate polls published last week, losing support from the December ballot to leftwing newcomers.

The Metroscopia poll in El Pais showed the Socialists winning 20.8 percent of the vote, behind the Unidos Podemos coalition with 25.4 percent, and the PP with 28.9 percent.

If a ruling majority cannot be formed after the June vote, Spaniards could potentially be forced to return to the ballot box for the third time in a year.

While the political impasse has had little effect on the country's economic recovery following years of prolonged recession, the Bank of Spain has warned stalled economic policy decisions could hit output if the situation continued.

(Reporting By Jesús Aguado; Editing by Clelia Oziel)