The Nikkei index closed at a record high on June 1 after gaining on optimism about the Middle East.
The benchmark index of 225 issues on the Tokyo Stock Exchange Prime section rose 604.83 points, or 0.91 percent, to finish at 66,934.33.
The gain came from Friday's close and marked a new record for the index.
The move followed positive developments related to the Middle East, according to market reports.
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Korean stocks opened sharply higher Friday following reports that the United States and Iran have reached an agreement to extend the current ceasefire.
Japan's Nikkei 225 Stock Average surged 5.6 percent to close at a record 62,833.84 on optimism about a potential U.S.-Iran agreement.
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The Nikkei average closed above 69,000 for the first time amid expectations that a deal to end the U.S.-Iran conflict would reduce turmoil in the Middle East.
Asian stocks reached a record high amid gains in technology shares and reduced geopolitical tensions. South Korea's SK Hynix achieved a $1 trillion market capitalization. Hopes for a US-Iran peace deal supported equity markets despite mixed US consumer confidence figures.
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Indian equities rose more than 1 percent on Monday amid optimism over a potential peace deal between the United States and Iran. Broader Asian stocks also posted modest gains following the news. Traders reduced bearish positions as crude oil prices eased.