The political committee formed by former President Barack Obama is preparing to mobilize for the 2018 midterm campaign, targeting more than two dozen congressional races and several key state elections with a program aimed at turning out Democratic-leaning voters.

The group, Organizing for Action, which emerged from the vestiges of Mr. Obama’s old campaign operation, intends to deploy organizers in 27 Republican-held congressional districts that could be key to a Democratic takeover of the House of Representatives. Their mission, officials with the group said, will be to coordinate and train volunteers and deploy them to help Democrats in states from California to North Carolina.

In addition, the organization will focus on several elections that may affect the redrawing of the congressional map after the 2020 census; these include races for governor in states such as Florida and Wisconsin and redistricting-themed ballot referendums in Colorado and Michigan. Organizing for Action previously announced it would partner in 2018 with a committee led by Eric H. Holder Jr., Mr. Obama’s former attorney general, to attack legislative gerrymandering in the midterms.

The new effort offers fresh insight into Mr. Obama’s political agenda for 2018: The Organizing for Action campaign emerged in part from a February meeting between the former president and strategists including Katie Hogan, the group’s executive director. In the meeting, Mr. Obama conveyed in no uncertain terms that recapturing the House and helping Democrats gain more influence in the redistricting process were two of his top goals, people familiar with the conversation said.