A plan to move more power lines underground in the District advanced a step Tuesday when Pepco and the District Department of Transportation formally asked city utility regulators for approval.

The project would take seven to 10 years and cost nearly $1 billion.

The plan would increase the average residential bill by $1.50 a month in the first year and no more than $3.25 a month after seven years, according to estimates by Pepco and city officials. More precise increases won’t be known until regulators at the Public Service Commission review a separate financing proposal expected to be filed in August, according to a joint statement from Pepco and the city.

The company and the District are seeking surcharges on bills to recover their investments, including the cost of debt service on $375 million in bonds the District will issue.

City officials will invest $62 million in capital improvement funds. Pepco will invest $500 million.

Moving the lines is aimed at reducing the number and duration of outages, Pepco and city officials said.

The plan involves work in manholes and on city streets, but the city will try to coordinate tear-ups with other utilities to limit disruptions, said Keith Foxx, program manager for the city’s transportation department and one of the officials and executives who discussed the plan Tuesday in a call with reporters.

Half of the city already has buried lines. The new plan would move overhead high-voltage lines that feed large sectors of the city that have been most affected by power losses. Those lines are in Wards 3, 4, 5, 7 and 8. Power lines that come directly down streets and connect to homes would remain above-ground.

The initial three-year cycle of work, for which the company has asked approval, affects an area with 30,000 customers, Foxx said.

In April, when Pepco agreed to be taken over by nuclear energy giant Exelon, the century-old local electrical company said it would stick to its plan to bury wires underground.

Moving big overhead lines is part of a continuing effort by Pepco to improve service. Calls for better performance arose from the public and regulators after a Washington Post investigation that showed the company ranked near the bottom for reliability in national studies and that equipment failures caused many lengthy outages even on clear days.