A quartet of congressional Democrats from Connecticut met Wednesday with General Electric CEO Jeffrey Immelt, trying to persuade the company to keep its headquarters in the state and improve GE’s strained relations with federal lawmakers.

U.S. Sens. Richard Blumenthal and Chris Murphy, along with 4th District Rep. Jim Himes, sat down with Immelt on Capitol Hill to specifically discuss GE’s uncertain future in the Nutmeg State.

The company’s Fairfield headquarters on Easton Turnpike is located the 4th District, which is represented by Himes, the meeting’s organizer. The corporation is the town’s largest property taxpayer.

The intervention comes amid rumblings that GE has felt slighted by the state’s congressional delegation, playing second fiddle to in-state rival United Technologies in a lucrative competition to supply the Pentagon with fighter jet engines.

“We wanted to make it clear to him that we were prepared to move heaven and Earth to keep GE in Connecticut,” Murphy told Hearst Connecticut Media.

Immelt met later with a dozen members of the New Democrat Coalition, a group that includes U.S. Rep. Elizabeth Esty, from the state’s 5th District, and vice-chaired by Himes, to discuss the company’s broader legislative agenda.

He was in Washington lobbying lawmakers to renew the charter of the U.S. Export-Import Bank, which GE relies on for money to finance its overseas operations. The bank’s reauthorization has run into opposition from majority Republicans.

A GE representative declined to comment Wednesday.

The talks between Connecticut trio and Immelt took place in the hearing room of the Senate Veterans Affairs Committee, on which Blumenthal serves.

“We had a productive meeting today while he was in D.C.,” Himes said in a statement. “During our discussion, I reiterated my strong support for GE keeping its headquarters in Connecticut and emphasized its long history here and the benefits that southwest Connecticut continues to offer.”

During the meeting, the lawmakers said, Immelt, a New Canaan resident, gave his assurances that no decision has been reached on a relocation.

“It was really a meeting among friends, but clearly GE is making a decision about its future not for the next 40 weeks, but the next 40 years,” Blumenthal told Hearst. “The meeting was extraordinarily amicable, but very agenda-driven and to the point.”

GE is expected to decide by year’s end whether it departs for another state. Even though the company is outside Esty’s district, she said she couldn’t pass up the opportunity to lobby Immelt to stay.

“When I had my chance to speak, I also flagged very grave concerns about the discussions about GE leaving Connecticut,” Esty said. “GE’s not only a flagship company for Connecticut, but for America. I want to prove to them that Connecticut is the right place for them to continue to do business.”

The source of GE’s discontent with Connecticut has been widely disputed among the state’s political class, with the company criticizing the state’s tax climate for businesses in June.

The rare public row followed the approval of a two-year $40 billion state budget along party lines that raises taxes on businesses and residents by $1.2 billion.

Minority Republicans have clamored for a special legislative session to reinstate a tax credit for net operating losses that was cut in half, as well as to roll back a requirement for companies to itemize how much of their earnings are tied to Connecticut. Both are reported to be highly important to GE.

“The discussions in Hartford are much more relevant to their decision than the discussions with the delegation,” Murphy said.

But top Democrats in Hartford, who control the Legislature and the governor’s office, say they aren’t to blame.

“I think he’s making a strategic decision if he chooses to leave Connecticut that really has very little to do with the budget that we’ve adopted and what is happening in Hartford, than what happens every day for GE in Washington, D.C.,” said state House Speaker Brendan Sharkey, D-Hamden.

Lawmakers like Sharkey have pointed to Congress’ 2011 snub of GE as the engine supplier for the Pentagon’s latest-generation fighter jet, the F-35 Joint Strike Fighter, as contributing to the rift.

The exclusive agreement could reap $67 billion for United Technologies Corp.-owned Pratt & Whitney, which manufactures its jet engines in the state, which GE does not. UTC’s Connecticut workforce is about 13,000, compared to a projected total of fewer than 1,000 GE employees in the state.

The number has been dwindling with the sale of GE Capital and other financial services divisions by the company.

“GE has made decisions to downsize its presence in Connecticut and that has an impact on how much clout they can expect from our delegation in Washington,” Sharkey said. “GE had an assumption that they should receive the same amount of attention and support as United Technologies.”

Asked about Sharkey’s comments, which were made to Hearst last Friday, Murphy said state and federal lawmakers need to work together.

“I think this has got to be a team effort to keep GE in Connecticut,” Murphy said.

The disconnect between Hartford and Washington over GE has become an uncomfortable subplot for Democrats in the state’s efforts to retain the company.

“The last thing in the world that we need right now is blame gaming,” Blumenthal said. “The state should be united and focused on seeking to keep GE, and we all ought to be pulling in the same direction.”