The findings contradict the findings of a survey released earlier this month by a rival company, Ipsos Reid, which found the Conservatives four percentage points ahead.
The Harris-Decima poll released late Wednesday by Canadian Press put the Liberals at 33 percent and the Conservatives at 32 percent. The same company found the Liberals ahead 31 percent to 30 percent a little more than a month earlier. The left-leaning New Democrats stand at 15 percent and the Greens at 6 percent.
Prime Minister Stephen Harper heads a minority Conservative government that was elected in January 2006. Last month he challenged Liberal leader Stephane Dion to either let the government's legislation pass or force an election by bringing his government down in Parliament.
No recent polls show any prospect for a majority government resulting from a near-term election, nor is it certain Harper would be reelected.
The Harris-Decima poll of just more than 1,000 Canadians was conducted from Aug. 7 to Aug. 10. It is considered accurate to within 3.1 percentage points 95 percent of the time.
