Mr. Morsi, who claims to be the only true Islamist in the race, faces his fiercest competition from a more liberal Islamist, Abdel Moneim Aboul Fotouh, a pioneering leader of the Muslim Brotherhood who was expelled from the group in June for arguing for a more pluralistic approach to both Islam and Egypt. He is campaigning now as the leading champion of liberal values in the race.

Both face a third front-runner, the former foreign minister Amr Moussa, who argued this week that Egypt cannot afford an “experiment” in Islamic democracy.

The winner could set the course for Egypt’s future, overseeing the drafting of a new constitution, settling the status of its current military rulers, and shaping its relations with the West, Israel and its own Christian minority. But as the Islamists step toward power across the region, the most important debate may be the one occurring within their own ranks over the proper agenda and goals.

Mr. Morsi’s conservative record and early campaign statements have sharpened the contrast between competing Islamist visions. The Brotherhood, the 84-year-old religious revival group known here for its preaching and charity as well as for its moderate Islamist politics, took a much softer approach in the official platform it released last year. It dropped the “Islam is the solution” slogan, omitted controversial proposals about a religious council or a Muslim president and promised to respect the Camp David accords with Israel. Its parliamentary leaders distanced themselves from the Salafis, ultraconservative Islamists who won a quarter of the seats in Parliament.

The Brotherhood’s original nominee was its leading strategist, Khairat el-Shater, a businessman known for his pragmatism. He had close personal ties to Salafi leaders, but he did not leave much of a paper trail besides an opinion column in a Western newspaper stressing the Brotherhood’s commitment to tolerance and democracy. Mr. Shater was disqualified last week because of a past conviction at a Mubarak-era political trial. In his short-lived campaign he stressed the Brotherhood’s plans for economic development and rarely, if ever, brought up Islamic law.