About a third, 35 per cent, are in favour of joining the military campaign in Syria and the rest were undecided, according to the poll published in El Mundo newspaper.
The poll - carried out after the November 13 suicide bomb and shootings in Paris - also found that 83 per cent of Spaniards believed a Paris-style attack could happen in Spain, suggesting that national security could emerge as a theme for a December 20 general election.
By contrast with the poll in El Mundo the survey showed more people supporting Spain "bombing the terrorists in Syria" than not, with 49.3 per cent in favour compared with 43.6 per cent against.
Several thousand people marched yesterday in Madrid against Spanish involvement in the Syrian conflict as conservative Prime Minister Mariano Rajoy stressed he would not rush into a decision.
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"No to war," chanted the demonstrators who gathered rallied outside the Reina Sofia museum in the Spanish capital. The organisers estimated their number at around 6,000.
"Decisions have to be well thought through, as in any aspect of life," said Rajoy, who added Madrid was in touch with its allies on a clear plan of action.
Leftist opposition parties have voiced opposition to Spanish military involvement in the Middle East.
The leader of the far-left grouping Podemos, Pablo Iglesias, backs putting the issue to a referendum.
Rajoy is mindful of how events unfolded in March 2004 under his Popular Party predecessor, former conservative prime minister Jose Maria Aznar.
Aznar's stance on Iraq was in stark contrast to that of the public in a traditionally pacifist country.