The poll asked local families if they would support an increase in the number of integrated places in Belfast, from 4% to 33%.
The NI Council for Integrated Education says the results reflect the opinions expressed by US President Barack Obama in his speech at the Waterfront Hall last week.
"On 17 June, President Obama threw down a gauntlet to the young people of Belfast, urging them to take the steps necessary to secure a shared and peaceful society by moving beyond segregated housing and segregated education," said Noreen Campbell of NICIE.
"This survey shows overwhelming support for NICIE's proposals to increase the volume of integrated primary school places in the BELB area from 4% to 33% even though this will mean an offset reduction in places in the controlled and maintained sectors that might impact on their own local schools."
Four hundred parents in the BELB area took part in the survey.
Just over 80% said integrated education is a vital part of creating a shared future - while 72% believe that funding for integrated education should be prioritised.
During his address in Belfast, which came ahead of the G8 in Co Fermanagh, the US President spoke to an audience of young people about ending divisions.
Barack Obama said: "If towns remain divided - if Catholics have their schools and buildings and Protestants have theirs, if we can't see ourselves in one another, if fear or resentment are allowed to harden - that too encourages division. It discourages co-operation."
He later visited Enniskillen Integrated Primary School with Prime Minister David Cameron.
Welcoming the outcome of Monday's survey, Ms Campbell added: "This poll gives voice to the parents of Belfast.
"The process of area based planning creates an opportunity for the voice of parents to be heard and for the development of a network of integrated schools to meet the stated demand for this type of education. This poll echoes the sentiments of President Obama and chimes with the public commitment to consolidating a peaceful society."