"We are on that path. We want to remain on that path, and we would obviously urge Kim Jong-un and his leadership team to sit back down at the negotiation table to do that," he said.
Esper made clear, however, that the US military stands ready to "fight tonight" if necessary.
"We have a full array of forces. They are ready. They're Air and Naval, Marine, Army forces. We have our South Korean partners with us, and then we have a broader set of allies and partners out there as well," he said. "So I'm confident in the readiness of our forces to deter North Korean bad behavior and should that fail, to fight and win as necessary."
Speaking to reporters at the Pentagon, Esper also said the US has been monitoring the situation very closely but would not say whether there have been indications of an imminent test or launch.
"I obviously don't talk about intelligence matters," he said.
Pressed to respond to Kim's threat to showcase a new strategic weapon, Joint Chiefs of Staff Chairman Gen. Mark Milley weighed in, "We'll see what happens.
"Our military defensive capabilities are adequate to defend the homeland." he added.
Questions have been raised about the readiness of South Korean and US forces in the wake of the allies' decision to scale back some joint military exercises in support of the diplomatic process.
North Korea denounces the drills as rehearsals for an invasion of the regime, and in his New Year's message, Kim complained that the allies continue to conduct their exercises despite what he said was a personal promise from US President Donald Trump to stop them.
Kim added that under such conditions he sees no reason to be bound by his self-declared moratorium on nuclear and ICBM tests.
Sen. Bob Menendez (D-NJ), ranking member of the Senate Foreign Relations Committee, disputed the effectiveness of downsizing the drills.
"I do believe that having canceled the military exercises was an enormous gift to Kim Jong-un without any benefit," he said in an interview with CNN.
The senator also accused Trump of having weakened the sanctions regime against North Korea.
"You have to engage China vigorously because China is probably the key to whether or not you can have a successful outcome with North Korea," Menendez said. "None of that, from my perspective, is going on right now."
Trump and Kim have had three meetings to try to reach a deal on dismantling North Korea's nuclear weapons program in exchange for US sanctions relief and security guarantees.
But negotiations between the sides have faltered since the leaders' second summit in Vietnam in February due to wide gaps over how to match their steps.
Trump said Tuesday following Kim's remarks that he still believes the North Korean leader will stick to his commitment to denuclearize.
"I think he's a man of his word," he said.
The same day, US Secretary of State Mike Pompeo told Fox News that the US hopes Kim will "take a different course."
"We're hopeful that Chairman Kim will make the right decision, (that) he'll choose peace and prosperity over conflict and war," he said. (Yonhap)