NEW YORK — A dispute between Mayor Michael R. Bloomberg and Gov. Andrew M. Cuomo over the $1 billion museum at Ground Zero has dragged on for so long that the museum will not open in time for the 11th anniversary of the Sept. 11 attacks — or even for the next one.

Aides to Bloomberg and Cuomo have so far been unable to resolve their differences over which government agencies will pay the operating costs of the museum, which is intended to document the terrorist attacks of 2001 and honor the nearly 3,000 victims. The two sides also remain at odds over who will have oversight of the museum and the surrounding memorial.

The negotiations are further complicated because Gov. Chris Christie of New Jersey must sign off on any agreement before it can take effect. Cuomo and Christie together control the Port Authority of New York and New Jersey, which owns the World Trade Center site. Bloomberg is chairman of the Sept. 11 foundation, which controls the National September 11 Memorial and Museum, and oversees commemorative events at the site.

With work on the museum at a standstill for nearly a year, fundraising and donations have fallen, and exhibits are gathering dust in fabrication shops in Buffalo, N.Y., and Santa Fe, N.M., according to museum executives.

The delay means that the museum may not open before construction on 1 World Trade Center is finished in early 2014.

Aides to Bloomberg and Cuomo said they hoped that the 11th anniversary, on Tuesday, might create pressure for a last-minute deal. Late last week, the two sides began circulating proposals to resolve the yearlong impasse.

Still, earlier agreements have fallen apart.

“It would be catastrophically sad if they can’t find a solution,” said Ira M. Millstein, a board member of the Sept. 11 foundation and a prominent commercial lawyer. “They really ought to sit down in a room and look at each other. It can’t be solved with emails.”

Other members of the board, whose relatives died in the attacks, said they would hold a demonstration Monday if the officials did not break the deadlock.

Bloomberg and Cuomo tried to bridge their differences last month when they agreed to establish an advisory committee to address disputes over the memorial, the museum and access to the site. But then a new dispute erupted over how much money the foundation would contribute to the museum’s operating costs, and the plan for the advisory committee has not moved forward.

Last week, in a break with custom, Cuomo and Christie did not attend the foundation’s annual fundraising dinner at Cipriani Wall Street, where the comedian Stephen Colbert was the host.

Port Authority officials bought a table for the event, but hesitated to attend because they were concerned about the reception they would receive from foundation executives, given the looming anniversary and the tensions over the negotiations, according to authority and foundation officials. Ultimately, at least two midlevel authority executives did go.

The first hint of tensions occurred after the 10th anniversary commemoration, when reports surfaced that Cuomo and Christie were annoyed at Bloomberg and the foundation over restrictions on access to the memorial and the ceremony. The reports were later denied by aides to the two governors.

The dispute entered a new stage in June with a struggle over who would control the overall memorial. The conflict over what many New Yorkers regard as a hallowed site carries political risks for the mayor and the governor.

Bloomberg has raised tens of millions of dollars for the museum and has contributed $15 million of his own money, but he may leave office at the end of 2013 with a legacy project in disarray. And Cuomo may be blamed for the standstill as talk of political dysfunction and a failed museum dominates news media coverage of the 11th anniversary.

The foundation, which has collected $450 million in private donations, estimates that it will take another year of construction work to complete the museum and two or three more months to install the exhibits and prepare for an opening.

Asked to explain the reasons for the impasse, Bloomberg’s aides would say only that negotiations were continuing.

“The delay is hugely disappointing to family members of victims and the many stakeholders who have worked hard to curate the museum,” said Julie Wood, a Bloomberg spokeswoman. “But we are confident that the finished product will be the definitive historical accounting of that terrible day.”

Josh Vlasto, a spokesman for Cuomo, said, “They are working through complex financial and economic issues, but we are cautiously optimistic” about an agreement.

The delay contrasts with advances on the rest of the site. The new signature skyscraper has reached its zenith at 104 floors, the mezzanine for the transportation hub is essentially complete, and the vehicle security center is nearing street level.

Officials say 4.5 million people have visited the Sept. 11 memorial since it opened a year ago. (The memorial covers eight acres at street level, while the 100,000-square-foot museum is seven floors below ground.)

The dispute over the museum represents a return to the political squabbling, delays and inaction that characterized the rebuilding of the 16-acre trade center site before 2008, when new leadership at the Port Authority forged an agreement on a construction plan.

But it also reflects the extraordinary costs of nearly every project at Ground Zero, including the skyscraper at 1 World Trade Center and the transportation center.

Under a 2006 agreement, the foundation was to raise $700 million to build the museum, including from private donations and state and federal money.

The Port Authority was responsible for building it and paying for hundreds of millions of dollars in related expenses. The authority is also required to formally lease or transfer the parcel to the foundation.

There has long been friction between the foundation and the authority over the rising costs of the project. The authority largely stopped construction after the 10th anniversary, arguing that the foundation owed it $150 million to $300 million.

Cuomo aides contended that the full cost of the museum had ballooned to $1.3 billion. The foundation countered that the Port Authority owed it more than $100 million because of the authority’s failure to complete the museum in 2009, as originally promised.

Subsequent negotiations between the mayor’s office and authority officials appointed by Cuomo reached what they thought was a tentative agreement in April 2012 in which the foundation agreed to pay the authority an additional $75 million and rent space at 1 World Trade Center.

But then Cuomo sought assurances that the foundation had a plan to cover the museum’s $60 million operating budget, saying that he did not want the authority saddled with additional costs in the event of a shortfall.

In recognition of the enormous public investment in the museum, the governor also sought some oversight of the memorial and the museum.

Executives at the foundation viewed Cuomo’s moves as a slap at Bloomberg, who became chairman and chief fundraiser for the foundation in 2006.

Late last week, foundation board members said they were trying to step up pressure on Bloomberg and Cuomo officials to resolve the impasse once and for all.

“People walk up to the doors of the museum, and the doors are locked,” said Christine A. Ferer, a board member whose husband, Neil D. Levin, the executive director of the Port Authority, died in the attack.

“Locked inside is the full story of 9/11.”