Prime Minister Mariano Rajoy's conservative Popular Party would win an election with 28.2 percent if the vote were it held today, up from 25.6 percent in April, the survey by the state run CIS research centre showed.
The Socialist Party would come in second with 24.9 percent support, compared to 24.3 percent during the last CIS survey published in April.
New anti-austerity party Podemos, a close ally of Greece's ruling Syriza, came in third place with 15.7 percent support, compared to 16.5 percent in April.
Podemos, which has been locked into a bitter contest with the Socialist Party to attract left-of-centre voters, had come in second place with 23.9 percent support in January, just ahead of the Socialists.
Both Podemos and the Socialists have sought to portray themselves as the only viable opposition to the Popular Party, which has ruled Spain since 2011.
The centrist Ciudadanos party also saw its support drop to 11.1 percent from 13.8 percent in April.
No clear majority would emerge from the vote, forcing the main parties to try to form a coalition, according to the poll, the nation's most closely-watched political survey.
Unemployment was Spaniards' main concern, followed by corruption.
Spain's unemployment rate of 22.4 percent s the second highest in the European Union after Greece's.
The poll was based on 2,486 interviews made across Spain between July 1 and 9.