Australia's ASX 200 index finished up 0.3% to 5,686.90, while South Korea's benchmark Kospi index closed down 0.2% to 2,073.31 points.
Weaker commodity prices weighed on Australian resource shares, with gold miners the hardest hit.
Gold fell to a five-year low on talks of a US interest rate rise this year.
The precious metal fell 4% to hit a low of $1,088.05 (Â£697) an ounce on Monday after its worst weekly performance since March last week.
Investors were also cautious with Greek banks set to reopen later in the day after being closed for three weeks.
German Chancellor Angela Merkel has called for swift aid talks so Athens can also lift withdrawal limits.
Chinese shares traded mixed despite data over the weekend showing that home prices rose for a second consecutive month in June.
Average new home prices rose 0.4% from May, when they were up 0.2% and marked the first monthly increase since April last year.
The Shanghai Composite closed up 0.9% to 3,992.11 - erasing earlier losses after the securities regulator denied reports that the government was considering how to end its support measures.
The mainland market has stabilized after Beijing pumped hundreds of billions of liquidity into the market through brokerages, mutual funds, and the state margin lender.
Hong Kong's Hang Seng index ended down 0.4% to 25,404.81 points.
Asian markets started the week largely unchanged on Monday with thin volumes, while Tokyo was closed for a public holiday.