The City Council has approved a $760 million project at Hilton Hawaiian Village that will add 550 time-share units, swimming pools, parking and retail space to the 22-acre resort in Waikiki.

Special management and planned development-resort permits were approved Wednesday despite objections from a family that leases to Hilton a portion of the land under the Diamond Head Tower.

"We are grateful for the vote of confidence provided today by the members of City Council and will continue to work with the Mun family to address their concerns as we move ahead with our project," Jerry Gibson, area vice president and managing director for Hilton Hawaii, said in a statement.

The Mun family says its property was included as part of the project without its knowledge or approval, attorney Cal Chipchase IV said.

"They found out about this project by accident," Chipchase said.

He sought a deferral of the permits to give the parties more time to settle issues related to the Muns’ access to their property, which they contend the development will affect.

Councilman Ikaika Anderson, the Zoning Committee chairman, urged the parties to continue working toward an agreement. Chipchase said he would discuss the matter with his clients.

Gibson said the Mun parcel is under one wing of the Diamond Head tower, and represents 11⁄2 percent of the resort’s acreage.

The project was supported by various local neighborhood boards and labor unions, who are hoping for the temporary and permanent jobs the project could bring to Waikiki and the tourism industry. It represents the biggest update of the hotel since it opened in 1955, and would nearly double the number of time-share units to 1,200 in the next 10 years.

The special management permit covers any development in coastal zones and allows Hilton to move ahead with obtaining the needed construction permits.

A planned development-resort permit outlines the conceptual plans for the project and the conditions under which it is approved.