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After the Supreme Court’s Citizens United ruling in 2010, however, the groups are able to run issue ads in attempts to sway voters. Democrats say that amounts to trying to buy elections.

Mr. McConnell, Kentucky Republican, said billionaires who back Democrats do the same thing.

“I wondered why he left out billionaire Tom Steyer, who plans to spend as much as $100 million pushing the issue of climate change in the 2014 election,” Mr. McConnell said in reply to Mr. Reid.

Philip Ellender, president of government and public affairs for Koch Companies Public Sector LLC, said Koch organizations are trying to defend American values, constitutional principles, and good-government tenets such as balancing budgets and limiting government regulations.

“We are disappointed that Sen. Reid is attacking private citizens rather than the problems facing this nation,” he said in a statement. “It is no wonder that Americans have lost faith in Congress.”

Koch representatives have denied many of Mr. Reid’s specific attacks, including the charge that a subsidiary did business with Iran. Koch says it followed all U.S. laws and even implemented a policy that was stricter than the law required.

Tuesday’s attack was the second in as many weeks for Mr. Reid. Last week, he accused a Koch-associated group, Americans for Prosperity, of running false ads attacking Obamacare.

“There are plenty of horror stories being told. All of them are untrue, but they are being told all over America,” he said, again identifying “the multibillionaire Koch brothers” as his target for criticism.

Later that day, Mr. Reid retracted part of his comment and said most, but not all, bad stories about the health care law were untrue.

Mr. Reid also has ended up in a poisonous back-and-forth with Sen. Chuck Grassley, Iowa Republican, in recent days. Mr. Reid, who led a move last year to change long-standing Senate rules on filibusters of presidential nominees, accused Mr. Grassley of flipping his position on whether votes on nominees should be delayed.

Mr. Grassley on Tuesday accused Mr. Reid of violating Senate courtesy and said it was the Democratic leader who blocked President George W. Bush’s nominees, then changed the rules when those same tactics were used against Mr. Obama.

The Senate has another set of nomination fights slated for Wednesday.