"Although the governor strongly disagrees with the court substituting its judgment for the constitutional process of the elected branches or a vote of the people, the court has now spoken clearly as to their view of the New Jersey Constitution and, therefore, same-sex marriage is the law," the statement said.
"The governor will do his constitutional duty and ensure his administration enforces the law as dictated by the New Jersey Supreme Court," it concluded.
On Friday, the Supreme Court in a 7-0 decision said, "the public interest does not favor a stay."
On Sept. 27, Superior Court Judge Mary C. Jacobson ruled in Garden State Equality v. Dow that the state's civil union law violates same-sex couples' civil rights by denying them federal benefits and protections.
The Supreme Court had planned to hear oral arguments in the Christie administrations appeal in January.
That will no longer be needed.
The legislature had previously passed measures legalizing same-sex marriage, but Christie vetoed them, saying it was an issue that should decided by a statewide referendum.
Same-sex marriage supporters praised Christie's decision.
"Gov. Christie's decision . . . is an unexpected but joyous development for the gay and lesbian couples who tied the knot at the stroke of midnight today and to the many more who will follow this week," said Udi Ofer, executive director of ACLU-NJ.
On his Twitter feed, President Obama posted: "Congrats, New Jersey. #LoveIsLove."
An opponent to same-sex marriage did not fault Christie for abandoing the appeal.
Len Deo, president of the New Jersey Family Policy Council.
"Obviously we're disappointed," said Len Deo, president of the New Jersey Family Policy Council. "The New Jersey Supreme Court has essentially tied the hands of Gov. Christie and continues to impose its idealistic view of what our culture should look like on unsuspecting New Jerseyans."
Given the court's decision Friday, he said, "it was pointless" to continue the appeal.
Staff writer Rita Giordano contributed to this article.