Forty-four percent of respondents to the poll conducted by Angus Reid Public Opinion, said they thought women should not have the right to abort a fetus after the first trimester, though just 5 percent think abortion should be banned outright.
Canada currently has no laws regulating a woman's right to have an abortion and the procedure is covered under the nation's healthcare system.
About 45 percent of Canadians said abortion should be limited to instances of rape, incest or to save the mother's life. More than 50 percent said they could envision at least some instances where the procedure should not be allowed.
The survey comes on the 25th anniversary of a Canadian Supreme Court ruling that denying a woman an abortion was unconstitutional.
The poll also indicates the appetite for a new debate over the nation's abortion policy is weak.
"Despite the fact that Canadians continue to have mixed personal feelings on abortion, and are divided on the way they perceive the legality and funding of the procedure, the appetite for true legislative action is lacking," the polling firm said in its analysis of the survey. "The proportion of Canadians who are unwilling to re-open the debate on abortion outnumbers that of those who believe a debate on the issue of overdue by a 2-to-1 margin."
The poll surveyed 1,009 Canadians Jan. 11-12 and has a margin of error of 3.1 percentage points.