By J.R. Wu and Faith Hung

TAIPEI (Reuters) - Taiwan's export orders fell less than expected in June, a relief for the island's many factories struggling with a slowdown in China and worried about the impact of Brexit on global trade.

Export orders contracted for the 15th straight month, but declines narrowed from China and Japan and rose from the United States and Europe compared with May.

June orders fell 2.4 percent from a year earlier, less than a 4.75 percent drop projected in a Reuters poll and improving from a 5.8 percent slide in May.

Taiwan's orders offer an indication of exports two to three months ahead and is a gauge of global technology demand.

Orders from the United States rose 1.2 percent, data from the ministry of economic affairs showed on Wednesday. Europe, which some analysts said accounts for about one-fifth of total orders, rose 3.2 percent.

"Brexit creates uncertainties in the financial environment and foreign exchange markets. Currently, we can't see an impact on our industry," Lora Ho, chief financial officer for Taiwan Semiconductor Manufacturing Co <2330.TW>, told reporters after the company's quarterly investor conference last week.

"It is likely to drag on for a very long time so we must continue to monitor it," Ho added.

TSMC is the world's top contract chip maker and an Apple Inc <AAPL.O> supplier.

Orders from China slipped 2.4 percent and from Japan, sank 16.4 percent.

Leading indicators, however, pointed to output expanding for the first time in three months as new export orders grew for the first time in six months. The Nikkei/Markit Taiwan Purchasing Managers' Index for June rose to 50.5 versus 48.5 in May.

(Editing by Jacqueline Wong)