Also weighing on sentiment was a report showing China's foreign direct investment slumped to a two-year low, adding to a series of downbeat data about the world's second largest economy.
But bargain hunting pushed Shanghai higher, gaining 0.57%, or 12.74 points, to an eight-month closing high of 2,239.47 while Hong Kong ended flat, edging up 0.52 points to 24,955.46.
Sydney gained 0.37%, or 20.6 points, to 5,587.1, but Seoul lost 0.49%, or 10.09 points, to 2,053.13 while Tokyo closed flat, inching up 4.26 points, to 15,322.60.
US shares rebounded late on Friday to end mixed after an early bout of selling on news that Ukraine had shelled Russian armoured vehicles after they entered its territory.
The Dow Jones Industrial Average ended down 0.30% at 16,662.91, after earlier having shed 0.50% on the news.
Worries that the incident would lead to a direct clash between the two ebbed after Moscow denied the incursion and Ukraine's foreign minister agreed to meet his Russian counterpart in Berlin on Sunday.
The two sides ended the "difficult" talks on the crisis with no concrete advances but "some progress", host Germany said, as clashes continued on the ground.
The nature of the progress was not disclosed by either party, but Germany's Foreign Minister Frank-Walter Steinmeier stressed the need for both nations to avoid "sliding ever deeper into a direct confrontation".
In currency markets, the dollar edged down to 102.32 yen in afternoon Asian trade, compared with 102.34 yen in New York late Friday.
The greenback is expected to gain in volatile forex trading this week, ahead of a speech on Friday by US Federal Reserve chief Janet Yellen at the central bank's annual economic policy symposium as investors look for any hint of a change to the Fed's interest-rate plans.
Last month, Mrs Yellen told Congress the Fed would hold its near-zero interest rate policy until the US economy strengthens, but may raise rates if the jobs market kept improving.
The euro bought $1.3393 and 137.05 yen against 1.3397 and 137.11 yen in US trade.
In oil markets, US benchmark West Texas Intermediate for September delivery was down 62 cents at $96.73, while Brent crude for October fell 92 cents to $102.61.
Gold traded at $1,302.78 an ounce at 0927 GMT compared to $1,313.53 an ounce late Friday.
In other markets, Taipei fell 0.71%, or 65.5 points, to 9,141.31. Taiwan Semiconductor Manufacturing Co was 0.81% lower at T$123.0 while Hon Hai Precision Industry was unchanged at T$108.0.
Wellington lost 0.14%, or 6.96 points, to 5,071.12. Genesis Energy was down 1.37% at NZ$1.80 and Spark was off 2.08% at NZ$2.82.
Manila gained 0.27%, or 19.07%, to 7,027.58. Top-traded Philippine Long Distance Telephone Co bucked the trend to fall by 0.43% to 3,236 points while Ayala Land Inc rose 1.88% to 32.60 pesos.