The surprise suggestion from the North's top military body, the National Defence Commission, was reported by the official KCNA news agency.
It was made hours after the nation confirmed its second missile test in recent days.
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Pyongyang also called for an end to live-fire drills and other hostile military activities near the disputed sea border in the Yellow Sea from Friday.
The maritime border is a frequent flashpoint. There have been no direct military clashes there since 2010 but the two sides intermittently fire warning shots or engage in live-fire drills.
The North also urged the South to scrap its annual joint military exercises with the United States slated for August, to create a favourable mood for this year's Asian Games in the South Korean city of Incheon.
Pyongyang has promised to send athletes to the games, to be held from September 19 to October 4.
Xi is visiting Seoul on Thursday and Friday for talks with President Park Geun-Hye before going on to Pyongyang.
China is North Korea's sole major ally and key economic benefactor, and the fact that Xi is visiting Seoul first has been seen by some as a deliberate snub.
Despite its leverage an increasingly frustrated China has failed to persuade the North to curb its nuclear weapons programme and to stop raising regional tensions through missile and atomic tests.
The North's latest olive branch followed a series of missile launches, including yesterday's test-launch of two short-range Scud missiles.
Pyongyang also announced separately Monday it would put two detained American tourists on trial on charges including "perpetrating hostile acts".
KCNA said suspicions about such acts by Matthew Todd Miller and Jeffrey Edward Fowle had been confirmed by evidence and their testimony.
Miller, 24, was arrested in April after he apparently ripped up his visa at immigration and demanded asylum in the communist state.
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