U.S. military exercises with the Republic of Korea (ROK) could be scaled back to aid diplomacy with the Democratic People's Republic of Korea (DPRK), Defense Secretary Mark Esper said on his way to Seoul, as Pyongyang said it was running out of patience.

The DPRK has long protested joint military drills, which it condemns as preparations for invasion, and has given Washington an end-of-year deadline to come up with a new offer in deadlocked negotiations on its weapons programs.

Read more: DPRK warns of retaliation against U.S.-ROK military drills

The U.S. and the ROK last year cancelled several joint drills in the wake of the Singapore summit between President Donald Trump and the DPRK leader Kim Jong Un, but are due to carry out a combined air exercise next month.

"We will adjust our exercise posture either more or less depending on what diplomacy may require," Esper told reporters on board his plane to Seoul, where he starts an Asian tour Thursday. 

The possible downsizing of the joint drills should not be seen as a "concession" to Pyongyang, he said, "but as a means to keep the door open to diplomacy."

"I'm all for diplomacy first," he added.

His comments came after Pyongyang reiterated its demands for the combined exercise to be scrapped.

"The U.S. is not accepting with due consideration the year-end time limit that we set out of great patience and magnanimity," a spokesman for the State Affairs Commission (SAC) said in a statement carried by the official KCNA news agency.

The SAC is the DPRK's top governing body and it is unusual for it to issue such declarations.

Holding the drills would be an "undisguised breach" of the Singapore summit declaration, it said, adding: "Betrayal is only what we feel from the U.S. side."

"We no longer feel the need to exercise any more patience," it went on.

Pyongyang has carried out a series of missile tests in recent weeks and months, including one launched at sea, which it said was fired from a submarine – a potential strategic game-changer. 

The tests would improve the DPRK's capabilities, Esper acknowledged. 

"Anytime you test, you learn something," he said. "We take them very seriously and we watch them very closely, but we're also not going to overreact and do something that, for example, could close the door to diplomacy." 

Esper will arrive in the ROK Thursday afternoon and meet with Seoul's Defense Minister Jeong Kyeong-doo Friday to discuss the two nations' security alliance.