But despite the overwhelming approval, 78 percent of the respondents worry about becoming victims of extrajudicial killings.
Rights groups, the United Nations and the United States have expressed concern over alleged extrajudicial killings under the campaign, resulting in expletive-laden responses from Duterte.
The nationwide poll, done on December 3-6, also found that indecision was the common sentiment among 1,500 adult respondents on the police claim that suspected drug dealers and users who were killed had resisted arrest.
Police are also investigating 3,993 additional deaths in the second half of the year, including possible vigilante killings in connection with the drug war.
The SWS poll was conducted between 3 and 6 December where 1,500 Filipinos across the country were interviewed face-to-face and the results were posted online on Monday (19 December).
Of these 32 percent were "somewhat satisfied" seven percent were undecided; five percent were somewhat dissatisfied and three percent were very dissatisfied.
Do they believe the police told the truth the suspects they killed resisted arrest?
Manila Auxiliary Bishop Broderick Pabillo, head of the Catholic Bishops' Conference of the Philippines (CBCP) Episcopal Commission on the Laity said, "we really need to worry about EJK even without the survey result".
Majority, however (42 percent) were unsure whether the police was telling the truth about victims putting up a fight during anti-illegal drugs operation.
According to the survey, 94 percent of Filipinos agreed it was "very" or "somewhat important" that drug suspects weren't killed indiscriminately during operations. Only three percent disagreed.
"We are thankful to the Filipino people for their continued expression of satisfaction on the Duterte administration's war against illicit drugs. But they would like less killings", Reuters cited Ramon Casiple, executive director of the Institute for Political and Electoral Reform, as saying.
"We recognize our people's concern as we assure them that the government's anti-drug operations are not aimed at poor, innocent, hapless individuals", Communications Secretary Martin Andanar said in a statement.
The survey, which had a margin of error of plus or minus 3 percent, also found 71 percent felt it was important to keep those suspected of drug use or drug trafficking alive.
"Killings under investigation are not state-sponsored", Andanar reiterated, "Many of these murders are perpetrated by common criminals wrongly attributed in news reports as part of police operations", he added.
"Murder is murder", he stressed.
Mr. Andanar asserted that the Duterte administration "respects the law and upholds the basic rights of our people, regardless of belief and political persuasion".