SEOUL, Sept 25 (Reuters) - North Korea is willing to consider another inter-Korean summit if mutual respect between the rivals can be assured, state news agency KCNA reported on Saturday, citing Kim Yo Jong, the sister of North Korean leader Kim Jong Un. The comment comes just a day after North Korea urged the United States and South Korea to abandon what it called their hostile policy and double standards towards it before formal talks can be held on ending the 1950-53 Korean War. The 1950-53 Korean War ended with an armistice not a peace treaty, leaving U.S.-led U.N. forces technically still at war with North Korea. The question of formally ending the war has been complicated by North Korea"s pursuit of nuclear weapons. "I think that only when impartiality and the attitude of respecting each other are maintained, can there be smooth understanding between the north and the south," Kim Yo Jong said. Constructive discussions offer the a chance for meaningful and successful solutions to issues including "the re-establishment of the north-south joint liaison office and the north-south summit, to say nothing of the timely declaration of the significant termination of the war", Kim said. Addressing the U.N. General Assembly on Tuesday, South Korean President Moon Jae-in repeated a call for a formal end to the war but later said time is running out to achieve such progress before his term ends in May. North Korea for decades has sought an end to the war but the United States has been reluctant to agree unless North Korea gives up its nuclear weapons. Kim, who is a powerful confidant of her brother the leader, said she noted with interest the intense discussion in the South over the renewed prospect of a formal declaration of the end of the Korean War. "I felt that the atmosphere of the South Korean public desiring to recover the inter-Korean relations from a deadlock and achieve peaceful stability as soon as possible is irresistibly strong," she said. "We, too, have the same desire." Expectations were raised that a declaration on ending the war, even if not an actual treaty, would be made during a historic summit between then U.S. President Donald Trump and North Korea"s Kim Jung Un in Singapore in 2018. But that possibility, and the momentum that the two leaders generated over three meetings came to nothing. Talks have been stalled since 2019. U.S. President Joe Biden said in his own U.N. address that he wanted "sustained diplomacy" to resolve the crisis surrounding North Korea"s nuclear and missile programmes. North Korea has rejected U.S. overtures to engage in dialogue and the head of the U.N. atomic watchdog said this week that its nuclear programme was going "full steam ahead".