LAGOS, Nigeria (AP) _ Eleven Nigerians, including three policemen, were killed today in shootouts between police and members of an outlawed Moslem sect in the eastern Nigerian center of Gombe, police said.

The semiofficial News Agency of Nigeria reported earlier that hundreds of people, including civilians, were feared dead in the shooting that began early today when police tried to arrest a leader of the Maitatsine sect, Yusufu Adamu.

In a statement this afternoon, the Nigerian police headquarters in Lagos said the shooting had ended, 11 people had been arrested and added,''Police have dislodged the fanatics.''

Six policemen were also wounded in the shooting which lasted most of the day, the police statement said.

Police mounted ''intensive patrols'' of Gombe, a city with an estimated population of 1 million in Bauchi state, 600 miles northeast of Lagos, it added.

The News Agency of Nigeria's correspondent in Gombe said troop reinforcements ringed the city - 150 miles from the border with Cameroon - and would allow no one in. Trucks packed with fleeing families and their belongings were seen leaving the city.

Police did not say whether Adamu had escaped in the shootouts between police and armed Maitatsine followers.

The Maitatsine sect was outlawed after rioting in 1980 in Kano, 200 miles northeast of Gombe and the center of the Islamic faith in Nigeria.

The Nigerian agency said the fighting began in the Pantami district of Gombe from where, it said, residents had begun leaving several days ago when Adamu and his followers turned up.

The shooting spread rapidly Friday to other parts of the city.

In a week of rioting by Maitatsine followers and clashes with police in March 1984 in the northeast Nigerian city of Jimeta, police reported 535 people killed. Nigerian newspapers put the toll at more than 700.

The sect's leader, Alhaji Marwa Maitatsine, a self-proclaimed prophet of Islam who rejected the teachings of the religion's founder Mohammed, was among 4,200 people killed in the 1980 violence at Kano.

In previous riots, members of the sect have been seen sprinkling themselves with what they call ''magic dust'' which they believe makes them immune to gunfire.