MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS fell 0.7 percent, but was still within reach of its June 9 peak, having risen 5.6 percent from its low after the Brexit vote on June 23.
Japan's Nikkei share average ended a six-day winning streak in thin trade on Tuesday after a stronger yen triggered profit taking, while bank shares underperformed on fears of counterparty risk following a fall in European bank stocks.
The Nikkei dropped 0.7 percent to 15,669.33 after gaining 5.5 percent in the course of its six day rally.
Activity in Japan's services sector contracted in June as new business shrank the fastest in almost five years, adding to worries that the economy is losing momentum due to weak consumer spending, a private business survey showed on Tuesday.
The Markit/Nikkei Japan Services Purchasing Managers Index (PMI) fell to 49.4 in June from 50.4 in May on a seasonally adjusted basis.
Stocks in China rose on Tuesday on further signs that growth in the country's services sector is speeding up, and as investors bought shares which are expected to benefit from reforms.
The Shanghai Composite Index gained 0.6 percent to 3,007.11.
Hong Kong stocks fell on Tuesday as investors locked in some of their profit after three straight sessions of gains with consumer staples and property stocks leading the slide.
The Hang Seng index fell 1.5 percent to 20,750.72
Reference: Reuters