The survey, carried out between June 16 and 23, showed the PP would get 140 seats in the 350-member lower house, down from 141 a week earlier.
The poll, commissioned by El Mundo newspaper, showed far-right party Vox, the PP's likeliest post-election ally, would get 35 seats, down from 36 a week earlier, Sigma-Dos said.
A likely coalition between Vox and PP would be one seat short of the 176 outright majority.
Sanchez on May 29 called a surprise snap election after his party and its junior coalition partner Podemos were routed in regional and municipal ballots.
Following the May municipal and regional elections, local negotiations between PP and Vox resulted in bickering in some cases.
Persons:
Alberto Nunez Feijoo, Isabel Diaz Ayuso, Jose Luis Martinez, Read, Pedro Sanchez's, pollster, Vox, Sanchez, Podemos, Yolanda Diaz, Inti Landauro, Angus MacSwan
Organizations:
People's Party, of, Almeida, El Mundo, Pedro Sanchez's Spanish Socialist Workers ' Party, PSOE, pollster Sigma, Sigma, Vox, Labour, Thomson
Locations:
of Madrid, Madrid, Retiro, Spain, MADRID, Pedro Sanchez's Spanish