Common Cause said in its complaints that the reported payment
to Stephanie Clifford, better known as Stormy Daniels, was an illegal in-kind campaign contribution.
The group's letter to Deputy Attorney General Rod Rosenstein called on the Justice Department to investigate potential violations of the law from the reported hush money, and in its letter to the Federal Election Commission lodged a similar complaint asking the agency to determine if a $130,000 payment from a limited liability company to Clifford was indeed an unreported, in-kind contribution to Trump's campaign.
The Wall Street Journal reported that Trump attorney Michael Cohen had formed a private LLC and paid Clifford $130,000 through the LLC weeks before the 2016 election so she would not go public with her story about an alleged sexual encounter in 2006 with Trump.
Cohen told CNN's Erin Burnett on Monday that "The Common Cause complaint is baseless, along with the allegation that President Trump filed a false report to the FEC."
Paul S. Ryan, vice president for policy and litigation with Common Cause, said on "Erin Burnett OutFront" that it was incumbent on the FEC and the Justice Department to investigate the matter.
"It certainly looks pretty obvious to me that this was hush money payment," Ryan said.
"If the money came from Trump's personal funds, that effectively establishes our allegation that his committee violated the law by failing to report an in-kind contribution and an expenditure," he later told CNN. "If it was Trump's own money, there was no illegal contribution -- but there's still a reporting violation."
CNN has not independently confirmed The Wall Street Journal's reporting, and Cohen said in response to the initial report that Trump denied "any such occurrence."
Larry Noble, general counsel of the nonpartisan Campaign Legal Center and a CNN contributor, said the FEC would consider the complaint and seek a response from the Trump campaign.
Noble predicted that based on the FEC's voting pattern in recent years, it probably would opt not to investigate the matter. Common Cause could then sue the FEC, at which point the agency would have to demonstrate why it had chosen not to investigate.
"I doubt they will investigate it," Noble said. "But you never know."
On the Justice Department side, Noble noted that a somewhat similar case had gone to trial for former presidential candidate John Edwards.
Jurors ultimately acquitted
Edwards on one count and were deadlocked on five others in the case, in which prosecutors accused Edwards of using illegal campaign contributions to keep his pregnant mistress under wraps as he ran for president in 2008.