ANKARA, May 14 (Reuters) - Turks started voting on Sunday in one of the most consequential elections in modern Turkey’s 100-year history, which could unseat President Recep Tayyip Erdogan after 20 years in power and halt his government’s increasingly authoritarian path.

The vote will decide not only who leads Turkey, a NATO-member country of 85 million, but also how it is governed, where its economy is headed amid a deep cost of living crisis, and the shape of its foreign policy, which has taken unpredictable turns.

Opinion polls give Erdogan’s main challenger, Kemal Kilicdaroglu, who heads an alliance of six opposition parties, a slight lead, but if either of them fail to get more than 50 percent of the vote there will be a runoff election on May 28.

The election takes place three months after earthquakes in southeast Turkey killed more than 50,000 people. Many in the affected provinces have expressed anger over the slow initial government response but there is little evidence that the issue has changed how people will vote.

Voters will also elect a new parliament, likely a tight race between the People’s Alliance comprising Erdogan’s conservative Islamist-rooted AK Party (AKP) and the nationalist MHP and others, and Kilicdaroglu’s Nation Alliance formed of six opposition parties, including his secularist Republican People’s Party (CHP), established by Turkey’s founder Mustafa Kemal Ataturk.

Polls opened at 8 a.m. (0500 GMT) and will close at 5 p.m. (1400 GMT). Under Turkish election law, the reporting of any results is banned until 9 p.m. By late on Sunday there could be a good indication of whether there will be a runoff vote for the presidency.

Kurdish voters, who account for 15-20 percent of the electorate, will play a pivotal role, with the Nation Alliance unlikely to attain a parliamentary majority by itself.

The pro-Kurdish Peoples’ Democratic Party (HDP) is not part of the main opposition alliance but fiercely opposes Erdogan after a crackdown on its members in recent years.

The HDP has declared its support for Kilicdaroglu in the presidential race. It is entering the parliamentary elections under the emblem of the small Green Left Party due to a court case filed by a top prosecutor seeking to ban the HDP over links to Kurdish militants, which the party denies.