South Korean President Moon Jae-In said that it is only a matter of time before the us and North Korea declare an end to their state of war on the Korean peninsula.
The war ended in 1953 with an armistice but a peace treaty was never signed.
Mr Moon, the son of North Korean refugees, also said there could be more diplomatic "bumps and bruises" as he tries to persuade Kim Jong-Un to give up his nuclear weapons.
But he described Mr Kim as "candid".
In an interview he also said he hoped European leaders would help him to mediate between Mr Kim and US President Donald Trump if negotiations stalled.
Mr Moon has met Mr Kim three times this year and has acted as a mediator between him and Mr Trump.
He said that he had had "ample discussions" with President Trump and other US officials about an end of war declaration.
Mr Moon said he wanted this to happen at the "earliest possible date" and he believed there was a "shared understanding between Washington and Seoul regarding this view".