Freddie Mac’s payments of roughly $500,000 to Davis Manafort, the people familiar with the arrangement said, began in late 2005, immediately after Freddie Mac and Fannie Mae disbanded an advocacy coalition that they had set up and hired Mr. Davis to run.

From 2000 to the end of 2005, Mr. Davis received nearly $2 million as president of the coalition, the Homeownership Alliance, which the companies created to help them oppose new regulations and protect their status as federally chartered companies with implicit government backing. That status let them borrow cheaply, helping to fuel rapid growth but also their increased purchases of the risky mortgage securities that proved to be their downfall.

The payments that Mr. Davis received for leading the Homeownership Alliance were reported in Monday’s issue of The New York Times. On Sunday, in an interview with CNBC and The Times, Mr. McCain responded to a question about that tie between Mr. Davis and the two mortgage companies by saying that he “has had nothing to do with it since, and I’ll be glad to have his record examined by anybody who wants to look at it.”

Image Rick Davis, left, with Senator John McCain in 2007. Credit... Stephan Savoia/Associated Press

Such assertions, along with McCain campaign television advertisements tying Mr. Obama to former Fannie Mae chiefs, have riled current and former officials of the two companies and provoked them to volunteer rebuttals.

The two people with direct knowledge of Freddie Mac’s post-2005 contract with Mr. Davis spoke on condition of anonymity. Four outside consultants  three Democrats and a Republican, also speaking on condition of anonymity  said the arrangement was widely known among people involved in Freddie Mac’s efforts to influence policy makers.

As president of the Homeownership Alliance, Mr. Davis received $30,000 to $35,000 a month. He, along with Fannie Mae and Freddie Mac, have characterized the alliance as a coalition of many housing industry and consumer groups to promote homeownership, but numerous current and former officials at both companies say the companies created and bankrolled the operation to combat efforts by competitors to rein in their business. The companies dissolved the group at the end of 2005 as part of cost-cutting in the wake of accounting scandals and, at Freddie Mac, a lobbying scandal that forced out its top Republican lobbyist.