South Korea's Kospi is among the biggest decliners, down 2.2 percent.
There are no major gains in China either. Shenzhen is down 1.1 percent, while Shanghai is unchanged. However, the Hong Kong-based Hang Seng bucks the trend, rising 0.4 percent.
The Tokyo Stock Exchange is closed for the weekend.
Although the US ceasefire proposal has been questioned, not least by Ukrainian President Volodymyr Zelenskyy, the oil market has reacted. On Monday, the price of North Sea oil (Brent) fell 1.8 percent to $102.9 per barrel, according to CNBC.
What do you think?