The development is likely to fuel growing scepticism over North Korea's commitment to a complete denuclearization of the Korean Peninsula as promised during last month's meeting between President Donald Trump and Kim Jong-un in Singapore.
Kim also voices hope "the invariable trust and confidence in Your Excellency Mr President will be further strengthened in the future process of taking practical actions".
The letter from Kim made no references to denuclearization, a key USA objective in its negotiations with North Korea.
North Korea accused the United States on Saturday of making "gangster-like" demands in the talks in North Korea, contradicting Pompeo who said the old enemies had made progress.
The ceremony came a day after talks between the United States and North Korea over the return of US war remains were postponed.
Trump met with Kim in Singapore on June 12-the first meeting between leaders of the two countries. The North then proposed meeting higher-level USA military officials Sunday, according to officials from the US and South.
North Korea had continued its nuclear and missile tests and stepped up its militant rhetoric through 2016 and 2017, and Kim and United States President Donald Trump had engaged in a spate of apocalyptic threats, taunts and name-calling just weeks before the Olympics.
Moon said he believed Trump and Kim would eventually make good on the promise made before the global community.
The president said in a tweet Thursday - exactly one month after his summit with Kim in Singapore - that "great progress" was being made in negotiations.
Pompeo was not granted an audience with Kim, and North Korea criticized USA demands following the visit.
Mr Shin Beom-chul, senior researcher at the Asan Institute for Policy Studies, said the peace declaration would have to be preceded by progress in denuclearisation talks between North Korea and the US. We agreed to the denuclearization of North Korea.
"I really think that we established a very good relationship", Trump said at a news conference in Brussels.
Earlier, three U.S. Forces Korea vehicles arrived at the Tongil Bridge near the border around 8:20 a.m. before putting United Nations flags on them and heading to Panmunjom.
South Korea said on Friday it had scrambled military jets to intercept two Russian military aircraft that entered the South's air defence territory four times through the day.
About 100 wooden transport cases were sent to the DMZ in recent weeks to prepare for receiving USA troop remains.