Some 47% of those polled were in favour of merging both Games, while 43% said the Paralympics should stay separate.
It is a controversial issue within the Paralympic movement with some athletes concerned the Games would "disappear".
Eight countries wanted to merge the Games while six wanted them separate.
The remaining five countries were divided on the issue.
Many of the countries with the most impressive medal hauls to date wanted to keep the Games split; they included China (67% separate, 27% integrated), the US (64%, 29%), and Australia (54%, 42%).
Continue reading the main story Canada - Yes: 55% No: 42% US - Yes: 64% No: 29% Chile - Yes: 19% No: 75%Peru - Yes: 43% No: 51%Mexico - Yes: 39% No: 46%France - Yes: 26% No: 70%Spain - Yes: 32% No: 64%UK - Yes: 50% No: 46%Germany - Yes: 46% No: 45%Turkey - Yes: 23% No: 42%Russia - Yes: 46% No: 39%Egypt - Yes: 39% No: 57%Kenya - Yes: 48% No: 51%Nigeria - Yes: 46% No: 50%India - Yes: 26% No: 47%Australia - Yes: 54% No: 42%Pakistan - Yes: 41% No: 37%Indonesia - Yes: 51% No: 37%China - Yes: 67% No: 27%However Germany, which also does well at the Olympics, broke away from this with 46% wanting to keep the Games separate while 45% wanted them to merge.
Nations preferring to merge the Games included France (26% separate, 70% integrated), Chile (19%, 75%), Egypt (39%, 57%), and India (26%, 47%).
This year's Olympics host, the UK, was divided over combining the Games, with 50% wanting them separate and 46% keen for a merger.
Polling was conducted for BBC World Service by the international polling firm GlobeScan and its research partners in each country. In five of the 19 countries, the sample was limited to major urban areas.
GlobeScan Chairman Doug Miller said: "The poll results suggest that integrating the Olympics and the Paralympics would be a controversial decision, with most of the nations who have won the lion's share of gold medals over recent years opposed to the change."
Baroness Tanni Grey Thompson said in December she was against a merger between both sets of Games.
The former Paralympic medal winner said the Paralympics would "disappear off the face of the earth" if a merger with the Olympic Games took place.
"That way we wouldn't have an opportunity to showcase the vast majority of sports like we do now," she said.
Grey Thompson, Britain's most successful Paralympian with 11 gold medals, added: "There is not a city in the world that could host a Games the size of the two combined.
"I'd rather invest time and effort in making sure that the Paralympics can be as parallel to the Olympics as possible."
A poll in January suggested that a majority of people in 18 out of 21 countries felt that the way their team performed at the Olympics was important to their national pride.
People in developing and middle-income countries get the greatest lift from Olympic achievements, according to the BBC Global Poll.