President Barack Obama and his aides plan to keep their presidential campaign machinery running to support his second-term agenda and will relaunch it in the coming days as a tax-exempt, nonprofit group.

The group will draw on one of the most valuable assets in American politics—Mr. Obama's large network of volunteers, along with its rich database of voter contacts—to stir support for the president's priorities, potentially focusing on immigration, climate change and gun violence, officials said.

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