The reactor at Yongbyon has been the source of plutonium for North Korea's nuclear weapons programme.
The White House said North Korea should "focus instead on fulfilling its international obligations".
The reactor was shut down in 2007 as part of a disarmament-for-aid deal.
But Pyongyang vowed to restart it in 2013, following its third nuclear test and amid high regional tensions.
White House spokesman Josh Earnest said the international community would not accept North Korea as a nuclear state.
"We will work with our partners in the context of the six-party talks to try to return North Korea to a posture of fulfilling those commitments that they have made," he said.
"We will repeat our call that North Korea should refrain from the irresponsible provocations that aggravate regional tension and should focus instead on fulfilling its international obligations and commitments."
Six-nation talks involving South Korea, the US, China, Japan and Russia aimed at ending the North's nuclear programme have been stalled since 2009.
Experts believe that, when fully operational, the Yongbyon reactor can make one nuclear bomb's worth of plutonium per year.
A US think-tank said this year that satellite images suggested work had started at the Yongbyon complex.
But Tuesday's announcement was the first official confirmation from North Korea that it had restarted operations there.
The state-run news agency KCNA said North Korea was improving its nuclear weapons "in quality and quantity".
It said that the North was ready to face US hostility with "nuclear weapons any time".
However, experts say North Korea's nuclear capabilities are unclear.
Pyongyang claims it has made a device small enough to fit a nuclear warhead on to a missile, which it could launch at its enemies. But US officials have cast doubt on the claim.
North Korea has made bellicose threats against its neighbours and the US before, often to coincide with annual joint military exercises held by South Korea and US forces.
The two Koreas remain technically at war, because the 1950-1953 war ended in an armistice, not a peace treaty.
The US has warned North Korea to refrain from "irresponsible provocation" after the communist state said its main nuclear facility had resumed normal operations.