A week after Republican Mark Greenberg called on U.S. Rep. Elizabeth Esty to limit the amount of outside spending on their race, a good government group called on her to do the same.

But Esty still isn’t interested.

About a week ago, she rejected Greenberg’s offer to limit the role of outside spending and on Friday, Common Cause of Connecticut encouraged Esty rethink her decision and negotiate a pledge with her Republican opponent to reduce outside spending in the race.

“Common Cause Connecticut appreciates Mark Greenberg calling for a People’s Pledge in Connecticut’s 5th Congressional District race,” Cheri Quickmire, executive director of Common Cause in Connecticut, said. “We encourage Congresswoman Esty to negotiate a pledge with Mr. Greenberg to reduce the role of outside spending in the race.”

On Sunday, Esty told an NBC reporter that she supports public financing, but it doesn’t exist at the federal level. She also supports a constitutional amendment to overturn Citizens United, the Supreme Court lawsuit that opened up the flood gates to third-party campaign spending.

“In this case, my opponent Mark Greenberg is sadly an example of what we’ve seen all too often in recent years, which is immensely wealthy people — people worth 50, 100, 200 million dollars,” Esty said, “who can self-finance whatever they want to do and that drowns out the voice of the American people.”

In 2012, when Esty first ran for the seat, she loaned her campaign $500,000 before the primary and $100,000 after the primary. Her campaign points out that Greenberg has spent $3 million on two failed campaigns for the seat. In 2012, Esty outspent her Republican opponent, Andrew Roraback, by about $1.6 million.

“I don’t take a pledge from someone who has pledged himself to spend millions of his own money,” Esty said Sunday on Decision 2014. “I can’t take very seriously his commitment to this.”

But Greenberg isn’t willing to give up on trying to convince the freshman Congresswoman.

“Elizabeth Esty is plain and simple a bald-faced hypocrite on campaign finance reform,” Bill Evans, Greenberg’s campaign manager, said. “She claims to be for campaign finance reform while rejecting every reform proposal . . . Esty has an opportunity to put her money where her mouth is on campaign finance reform.”

Greenberg offered that they wouldn’t have to go cold turkey on the outside funding, but they could at least negotiate a limit.

“If Elizabeth is sincere, she will agree to a spending cap of $1.28 million, more than enough to communicate our respective messages,” Greenberg has said.

On Sunday, Greenberg was also on WFSB’s Face the State and he talked about how the system of funding politics is broken.

“The second a person gets elected they’re making calls for fundraising,” Greenberg said. “They don’t have time to read the bills . . . the system has become out of control in terms of the money.”

He said that’s why he called on Esty to advocate for the removal of “dark money” or some “cap of the money that’s spent.” He said he just wants “an equal playing field.”

The pledge Greenberg is encouraging Esty to take would be similar to one negotiated in 2012 in the Massachusetts race for U.S. Senate between Republican incumbent Scott Brown and Democratic challenger Elizabeth Warren to discourage attack ads funded by outside groups.