ABUJA, Nigeria (CNN) -- The centrist Peoples Democratic Party made a strong showing in local elections over the weekend, leaving it in a position to dominate the country's planned transition to civilian rule in May.

The party appears to have won control of about 60 percent of races in 774 local districts, based on results from 647 of those districts. The PDP is led by veteran politicians, many of whom opposed former military strongman Sani Abacha.

Abacha died in June. His successor, Gen. Abdulsalami Abubakar, has promised to step down after elections next May. Nigeria has been ruled by military governments for all but 10 of the 38 years since it won independence from Britain.

The PDP held a lead over the conservative All Peoples Party, which took about 25 percent of the races, with the left-of-center Alliance for Democracy in third place. Those parties automatically qualify for a place on the ballot in next year's parliamentary and presidential elections.

Turnout was generally high for the elections, which marked the first step in the 56-year-old Abubakar's plan to ease the army's grip on power.

"Democracy is here to stay and it will stay," Abubakar told visiting U.S. Commerce Secretary William Daley, the most senior U.S. representative to come to Nigeria since the army annulled elections in 1993 that were regarded as free and fair.

Voting proceeded peacefully in most of the country, although local newspapers said up to 14 people died in several incidents -- most in the oil-producing Niger Delta where clashes occur almost daily.

Nigeria's last military ruler to give up power to an elected government, Gen. Olusegun Obasanjo, is now a PDP candidate for president.

"I am encouraged more than ever before by the local government elections to persevere on the path of seeking the mandate of our people and to serve Nigeria as the next elected president," Obasanjo, 61, said after the vote.

The Commonwealth, which suspended Nigeria after Abacha ordered the execution of author Ken Saro-Wiwa and eight other minority rights activists in 1995, said it was satisfied with the conduct of the vote and delighted at public enthusiasm.

The association of Britain and its former colonies is now led by a Nigerian, Secretary-General Emeka Anyaoku. Anyaoku said the results "bode well" for next year's balloting.

Reuters contributed to this report.