The privately run research group TNS Lanka said close to 75 percent of people questioned said they are "firmly in favour of military action, seeing it as the only route to wipe out terrorism."
More than half the respondents also believed the war -- which has been raging in varying degrees of intensity since 1972 -- will be over by the end of next year.
Some 91 percent of those polled did not believe the separatist Liberation Tigers of Tamil Eelam (LTTE) represented the minority ethnic Tamil community.
The group questioned 500 people living outside the northern conflict zone between October and November.
The result will be greeted by the government as an endorsement of its decision in January to pull out of a Norwegian-brokered truce with the LTTE and escalate its offensive.
Sri Lankan President Mahinda Rajapakse has said he will not accept anything