According to Friday reports, around 90 percent of the ballots have been counted so far and Morsi is leading with 25 percent.
Former prime minister of Mubarak’s regime Shafiq is in the second place with 23 percent based on results from 12,800 polling stations out of 13,100.
Official results from the country’s electoral body are expected to be announced next week.
The two candidates will go to a second round run-off vote on June 16 and 17.
Some 50 million eligible voters were given the chance to choose between candidates.
Turnout was around 50 percent over the two days of voting on Wednesday and Thursday, electoral commission officials said.