“They’re obsessed,” Jim Messina, President Obama’s campaign manager, recently wrote of the billionaire Koch brothers and their attacks on the president, in a fund-raising letter to supporters. The same might be said of both sides after Mr. Messina on Wednesday lobbed another anti-Koch rocket, this one to a Koch Industries company executive.

Mr. Messina challenged Philip Ellender, Koch’s president for government and public affairs, to see to it that the conservative anti-Obama group Americans for Prosperity discloses its donors — to prove Koch’s contention that it is financed by tens of thousands of grass-roots Americans, not a few oilmen and special interests, as the Obama campaign has suggested.

“It is a cynical stretch to describe the political activities of your employers as furthering democracy when they are courting huge checks from special interest donors to pay for negative ads, with no public disclosure of the identity of those donors,” Mr. Messina wrote in the letter to Mr. Ellender that the campaign released, and which was first reported by The Washington Post.

Mr. Messina was responding to a letter from Mr. Ellender sent on Friday that objected to Mr. Messina’s criticism of the oilmen Charles and David Koch in the campaign’s fund-raising appeal earlier that day. Mr. Ellender disputed Mr. Messina’s claims that Koch Industries refineries had helped raise gasoline prices, that the company had “committed $200 million to try to destroy President Obama” and that it finances Americans for Prosperity.

“It is an abuse of the president’s position,” Mr. Ellender wrote, “and does a disservice to our nation for the president and his campaign to criticize private citizens simply for the act of engaging in their constitutional right of free speech about important matters of public policy.”

Mr. Messina reiterated his claims in the response to Mr. Ellender on Wednesday.