The term of the minority government led by his center-right People’s Party (PP) expires in 2020, but 55 percent of respondents in Monday’s survey said they wanted a ballot before then.
The figure in an equivalent survey in October was 49 percent.
The poll was taken by pollsters Metroscopia for newspaper El Pais newspaper between Nov. 6 and 8 as former Catalan president Carles Puigdemont -- whose government was sacked by Rajoy -- pursued his campaign for the region’s independence from self-imposed exile in Belgium.
Authorities in Madrid have called an election in Catalonia for Dec. 21.
Rajoy was given a second term in October 2016 when the PP won the most votes but failed to take a parliament majority.
The PP’s weakness in parliament has meant the government has struggled to pass legislation, including the 2018 budget.
Slideshow (3 Images)
Support for the PP, if the elections were held today, slipped to 26.1 percent in November from 26.9 percent in July.
Backing for Ciudadanos (Citizens), a pro-Spanish unity party originally from Catalonia, jumped to 22.7 percent from 18.5 percent, putting it equal second with the Socialists.
The poll reflected an official survey taken at the beginning of October that showed support for Ciudadanos had risen during the Catalan crisis, which has become Spaniards’ second-largest issue of concern after unemployment.
Left-wing Podemos, which supports a negotiated referendum on Catalan independence, saw voting intentions drop to 14.7 percent from 18.7 percent previously, the Metroscopia poll showed.
More about: #Spain