The government and opponents of the base relocation have been locked in a legal battle, where both sides have sued each other, AP reported.
Abe said that his government is accepting a court proposal not to force the reclamation work over Okinawa's objections. The court in February made the proposal as an interim step allowing talks. Details of the proposal were not made public.
Okinawa Gov. Takeshi Onaga last year issued an order to suspend permission for the reclamation work. Then the central government sued to reverse the order, to which Okinawa counter-sued, seeking a court injunction.
The work involves filling in part of a bay to create off-coast runways for Futenma air station, which is now in a more densely populated area.
Abe said the plan to eventually move the base to the town of Henoko is unchanged. The relocation is based on a 20-year-old bilateral agreement to reduce the burden of the US military presence on Okinawa.
Opponents want the base moved off Okinawa entirely, and a prospect for a compromise is still unclear.
The sudden reversal of the central government's policy to continue with the reclamation work is seen as a vote-buying attempt ahead of this summer's parliamentary elections.
Abe said he wants to avoid leaving the situation deadlocked "for years to come, a development that nobody wants to see."
He said his government will proceed with talks with Okinawa "toward an amicable settlement" under the court's proposa. Okinawa has agreed to accept the proposal, and is expected to drop the lawsuit.