Hillary Clinton called Friday for rethinking President Obama’s strategy to combat North Korea’s nuclear program, saying the country’s latest nuclear test gave the White House “an opening” to expand sanctions and broaden a missile-defense program in neighboring countries.

She also said that the United States can do more to pressure China to lean on North Korea, its longtime ally, to halt its program.

“It’s clear that the increasing threat posed by North Korea requires not only a rethinking of the strategy, but an urgent effort to convince the neighbors, most particularly China, that this is not just a U.S. issue,” Mrs. Clinton said, signaling she would support a change in strategy since she served as secretary of state.

Since the start of the Obama administration, Mrs. Clinton had supported Mr. Obama on his “strategic patience” approach of gradually escalating sanctions on North Korea, but the blast on Friday signaled that the tactic had failed to halt North Korean advances in developing its nuclear capacity.