TOKYO, July 1 (Reuters) - Japanese manufacturing activity barely expanded in June despite a strong pick-up in export demand, a private survey showed on Wednesday, adding to fears of a sharp slowdown in economic activity in the second quarter.

The Nikkei/Markit/ final Japan Manufacturing Purchasing Managers Index (PMI) was 50.1 in June, higher than a preliminary reading of 49.9.

The index remained just above the 50 threshold that separates expansion from contraction, but indicated that growth slowed from the previous month, when the PMI index was 50.9.

The index for new export orders rose to 54.0, more than a preliminary 53.6 and more than 50.6 in the previous month, to show the fastest increase since December 2013. Some companies reported a weaker yen was helping to improve price competitiveness, while other cited better sales to China and Europe.

New domestic orders fell to 49.6, versus the flash reading of 49.4 and 50.9 in May.

The output component of the PMI index was 50.9, above the flash reading of 50.5 but below 51.9 in the previous month.

Economists are already forecasting much slower economic growth in April-June as manufacturers curb production to lower stubbornly high inventories.

Data earlier this week showed an larger-than-expected decline in industrial output in May, leading some analysts to say the risk of an economic contraction in the current quarter cannot be ruled out.

Firmer export orders, however, could fuel hopes for an improvement in the second half of the year.

(Reporting by Stanley White; Editing by Kim Coghill)