• China released its official PMI figures on the weekend, with its manufacturing PMI coming in at 49.5, unchanged from May and marking its second straight month in contraction territory.
• A private survey of manufacturing activity in China, however, diverged from the official numbers, showing the sharpest improvement in business conditions in three years.
• On Monday, Japan revised its first-quarter GDP contraction to 2.9% year on year, from 1.8% reported earlier.

Asia-Pacific markets started the second half of the year on a positive note as investors assessed June business activity data from China as well as Japan's business confidence readings.

China released its official PMI figures on the weekend, with its manufacturing PMI coming in at 49.5, unchanged from May and marking its second straight month in contraction territory.

A private survey of manufacturing activity in China, however, diverged from the official numbers, showing the sharpest improvement in business conditions in three years. The S&P Caixin PMI climbed to 51.8 in June compared with 51.7 in May.

On Monday, Japan revised its first-quarter GDP contraction to 2.9% year on year, from 1.8% reported earlier. GDP data for the third and fourth quarters of 2023 were also revised downward.

In a technical note, the country's cabinet office said the revision was due to new construction investment data.

Japan's Nikkei 225 rose 0.12%, closing at 39,631.06 while the the broad-based Topix climbed 0.52% to 2,824.28, reaching a new 34-year high. The Nikkei earlier hit a three-month high during the session, before paring gains.

Confidence among big Japanese manufacturers improved in the second quarter, with the Bank of Japan's Tankan survey at +13 compared to +11 in the first quarter. Economists polled by Reuters had expected it to be at +12.

Non-manufacturers' sentiment stood at +33, matching market forecasts and down from +34 in the previous quarter. This was also the first time in four years that confidence among non-manufacturers worsened.

South Korea's Kospi was up 0.23% and ended at 2,804.31, near its 31-month high of 2,807.63, but the small-cap Kosdaq advanced 0.8% to 847.15. The country saw its factory activity expand at its fastest pace since February 2022, with its June manufacturing PMI up to 52.0 from 51.6.

Mainland China's CSI 300 climbed 0.48% to 3,478.18, and Australia's S&P/ASX 200 fell 0.22% to 7,750.7, the only major index in negative territory.

Hong Kong markets were closed Monday for a public holiday.

Overnight in the U.S., all three major indexes ticked down as traders looked at a "near perfect" set of inflation data, according to an industry expert.

Inflation in May slowed to its lowest annual rate in more than three years, with the core personal consumption expenditures price index, up just 0.1% last month and 2.6% higher from the prior year and in line with Dow Jones estimates.

The core PCE index, which strips out prices of food and energy, is the Federal Reserve's preferred inflation measure. Headline PCE, which includes food and energy, was flat on the month and up 2.6% on an annual basis — also in line with expectations.

"From the market's perspective, today's PCE report was near perfect," said David Donabedian, chief investment officer of CIBC Private Wealth U.S. "This was unambiguously a positive report."

The S&P 500 slid 0.41%, while the Nasdaq Composite declined 0.71%. The two averages hit new all-time intraday highs earlier in the session before pulling back. The Dow Jones Industrial Average dropped 0.12%.

—CNBC's Hakyung Kim and Alex Harring contributed to this report.