The data, collected by the Sociological Research Center (CIS), predicted that the PP would secure 24%.
Centre-right part Ciudadanos would move into second position, narrowly overtaking the Socialists with 22.4% to 22% respectively.
Anti-austerity Podemos would take 19.6%.
A previous poll published in February showed the PP taking 26.3%, Socialists 23.1% Ciudadanos 20.7% and Podemos 19%
The PP currently holds a minority in parliament following the 2016 general election with Spaniards expected to return to voting booths in 2020.