England and Mexico fell victim to howlers by officials in their second-round matches on Sunday, prompting an apology from FIFA president Sepp Blatter.
Blatter, who rejected the use of goalline technology just three months ago, said the game's governing body would now look again at the issue, although he ruled out using video replays.
The New York-based Nielsen Company surveyed 27,000 people in 55 countries on questions related to football's biggest event, including whether referees should have video replays to help them make close calls.
Sixty-five percent of them backed the use of video replays at the World Cup. Only about one in 10 respondents said the ban should stay, while the rest were undecided, the research company said in a statement.
Technology is already used in other major sports such as cricket and tennis.
Nielsen's online poll showed regional support for video technology to be used at the World Cup was strongest in South America, where 79 percent respondents thought FIFA should change its position.
However, in Ireland, whose team lost a play-off to reach the World Cup finals after an infamous handball by France's Thierry Henry, 84 percent of people said video assistance was a good idea.
The company said online discussion about video replays soared after the refereeing decisions that hit England and Mexico at the weekend.
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