Kim Kye Gwan, a North Korean diplomat who once represented Pyongyang at the Six-Party Talks in Beijing, said any U.S. request for "new talks" should come with conditions, including a departure from previous tactics, South Korean news agency Yonhap reported.
"If the United States truly does not want to let go of dialogue with us, it must first withdraw from the hostile policy of regarding us as the enemy," Kim said in the statement that was issued late Monday, local time.
Kim claimed North Korea has "received nothing in return" for summits with Trump.
"We will not give anything away that would give the U.S. president something to brag about," the North Korean official said. "We must receive back what President Trump has claimed proudly as his achievements."
On Sunday morning, Trump had tweeted about North Korea, and recent North Korean comments about Democratic presidential candidate Joe Biden.
"Mr. Chairman, Joe Biden may be Sleepy and Very Slow, but he is not a "rabid dog." He is actually somewhat better than that, but I am the only one who can get you where you have to be. You should act quickly, get the deal done. See you soon!" Trump tweeted.
Choson Sinbo, the pro-Pyongyang newspaper published in Japan, said a third Trump-Kim summit raises the possibility of a U.S. presidential visit to the capital Pyongyang.
The newspaper, run by North Korea's de facto embassy in Japan, also stated Trump has "no option" but to accept North Korean demands.
North Korea could be making preparations ahead of more meetings.
Kyodo News reported Monday North Korea's first vice foreign minister Choe Son Hui had left for Russia.
Choe could be visiting Moscow for talks about future U.S.-North Korea negotiations on denuclearization, according to the report.
Meanwhile, Kim supervised a parachute landing exercise held by the country's air force "under the simulated conditions of real war," state-controlled Korean Central News Agency reported Monday morning.