By Chris Francescani

NEW YORK (Reuters) - A deal has been reached to resume construction on a National September 11 Museum in New York, Mayor Michael Bloomberg said on Monday on the eve of the 11th anniversary of the attacks on the World Trade Center towers.

A cost dispute between the foundation that controls the museum and the Port Authority of New York and New Jersey, which is building the ambitious subterranean structure, has halted construction of the project for months.

Diverging estimates on the cost of the project, which had been scheduled to open this week prior to the delays, from each side range from $700 to more than $1 billion.

"I'm very gratified that on the eve of this important anniversary we are able to announce an agreement that will ensure the completion of the 9/11 museum," Bloomberg's statement said.

"My goal during this period has been to get construction of the museum restarted. This agreement ensures that it will be restarted very soon and will not stop until the museum is completed," he added.

The museum is designed to extend seven levels underground and will include artefacts from the day of the attacks, from firefighters' helmets to pieces of rubble to models of the site before the attacks, which killed 2,751 people in New York.

Bloomberg chairs the National September 11th Memorial and Museum foundation. The Port Authority is controlled by Governors Andrew Cuomo of New York and Chris Christie of New Jersey.

Under the agreement, representatives for all three will participate in a committee that oversees annual events, including Tuesday's September 11th ceremony.

The foundation had said in July that politicians would be excluded this year from speaking roles at the ceremony to focus on victims' families, who traditionally read the names of the dead. In the future, that decision will be made by committee, not just the foundation.

Under the deal, the Port Authority's cost obligations will be reduced by more than $150 million. Construction of the museum, however, must begin soon and continue until it is completed. The project is expected to take more than a year. (Editing by Cynthia Johnston and Todd Eastham)

• A Permanent Economic Emergency