Parliament Speaker Mohammed Baqer Qalibaf and principlist Saeed Jalili are trailing with 16.9 percent and 16.3 percent respectively, according to the survey.
Amir-Hossein Ghazizadeh Hashemi, with 3.2 percent, Alireza Zakani, 1.2 percent, and Mostafa Pourmohammadi, 0.5 percent, have slim chances of gaining the votes, the research center predicted.
However, the possible game changer is that 28.5 percent of the respondents are still undecided and have not chosen their favorite candidate, the results showed, adding 3 percent said that they will vote blank.
50.3 percent of the respondents in the survey were male and 49.7 percent were female. 40.1 percent were in the 18 to 35 year-old age category, 46.1 percent were between 36 and 60 years old, and 13.8 percent were above 60 years of age.
Meanwhile, 40.3 percent of the respondents live in provincial capitals, 9.36 percent live in towns, and 8.22 percent in rural areas.
The research center used simple random sampling and a pool of 1100 pollsters to gather the data. The results have a 95 percent accuracy with a 3 percent margin of error.
Iranians will go to the polls on Friday to elect a successor to the late President Ebrahim Raisi who died in a helicopter crash on May 19 along with his accompanying delegation.