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.
Seoul's benchmark Kospi index briefly topped 6,700 points on Tuesday, hitting a new intraday record driven by large-cap tech shares. The gain came ahead of first-quarter earnings from US big tech firms such as Alphabet and Meta. As of 9:15 a.m., the Kospi stood at 6,656.05, up 41.02 points or 0.62 percent.
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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.