Maximize Offshore Resource Exploration Act of 2013 or MORE Act of 2013 - Declares without force or effect all federal prohibitions against the expenditure of appropriated funds to conduct natural gas leasing and preleasing activities for any area of the Outer Continental Shelf (OCS).

Revokes all withdrawals of federal submerged lands from leasing for oil and natural gas exploration and production.

Amends the Outer Continental Shelf Lands Act to prohibit the Secretary of the Interior from granting an oil or natural gas lease for any OCS located within 25 miles of a state coastline unless the state has enacted a law approving the issuance of such leases by the Secretary.

Sets forth an allocation schedule for a: (1) 75% state share of revenues derived from U.S. royalties under qualified oil and gas leases on submerged lands located within the seaward boundaries of a state, and (2) 90% state share of revenues derived from royalties under leases that are located within 25 miles of the coastline of a state and within the seaward boundaries.

Extends the jurisdiction of state civil and criminal law, as appropriate, to the Alaska, Pacific, Gulf of Mexico, and Atlantic OCS Region State Adjacent Zones and OCS Planning Areas.

Establishes a separate account in the Treasury to be known as the Renewable Energy Reserve, consisting of 12.5% of revenues derived from U.S. royalties under such oil and gas leases located within the seaward boundaries and 5% of revenues derived from leases located within 25 miles of the coastline of a state and within the seaward boundaries.

Makes the Reserve available to offset the cost of subsequently enacted legislation to: (1) accelerate the use of cleaner domestic energy resources and alternative fuels; (2) promote the utilization of energy-efficient products and practices; and (3) increase research, development, and deployment of clean renewable energy and efficiency technologies and job training programs for those purposes.