Mr. Braynard said the idea is to create “the Acorn of the right” — a reference to the liberal community organizing juggernaut that was largely dissolved after a 2009 scandal sparked by a conservative provocateur’s sting videos.

Mr. Braynard and Mr. Chrabaszcz worked together starting in the late 1990s at the Republican National Committee building and deploying the party’s national voter database. They reunited on the Trump campaign in 2015, at a time when Mr. Trump was widely believed to have little chance of winning the presidency. Mr. Braynard left the campaign in March 2016 amid an internal dispute, but remained supportive of Mr. Trump. Mr. Chrabaszcz remained employed by the campaign through Election Day, and did some consulting work for the campaign as recently as January.

Their new group is registered under a section of the tax code — 501(c)(3) — that allows it to raise unlimited funds from donors without publicly disclosing their identities, but also bars it from engaging in partisan politics. The prospectus declares that “our targeting is not based on political party affiliation or to benefit any particular candidate,” though Mr. Braynard conceded that the people his group hoped to engage were not dissimilar from those who mobilized by Mr. Trump’s campaign.

Mr. Braynard stressed that the effort to clamp down on alleged illegal voting is secondary.

But it could attract criticism from voting rights advocates. They say there’s little evidence of widespread voter fraud, and contend that the real goal of conservative efforts to fight illegal voting — including the Trump administration’s investigation of alleged voter fraud — is to purge Democratic-leaning African-American and Hispanic voters from the voter rolls.

Representatives from the White House, the Republican National Committee and Mr. Trump’s re-election campaign did not respond to requests for comment on Look Ahead America.

The project in some ways stems from an idea that Mr. Braynard articulated before the 2016 Republican primaries in a memo to the Trump campaign leadership, in which he urged them to focus on “enfranchising the conventionally low propensity voters that support our candidate.”

It is unclear to what extent Mr. Trump’s general election victory over Hillary Clinton relied on such voters.