WASHINGTON (Reuters) - U.S. inventories rose moderately in June as sales recorded their biggest increase in nearly 3-1/2 years, suggesting businesses were making progress reducing an inventory overhang that has weighed on economic growth since last year.

The Commerce Department said on Friday inventories increased 0.2 percent after a similar gain in May. Sales shot up 1.2 percent in June, the largest rise since February 2013, after rising 0.3 percent in May.

At June's sales pace, it would take 1.39 months for businesses to clear shelves. That was the fewest number of months since November 2015 and down from 1.40 months in May.

Economists had forecast inventories, a key component of gross domestic product, edging up 0.1 percent in June after a previously reported 0.2 percent gain in May.

Retail inventories increased 0.5 percent in June, as estimated last month in an advance report. Retail inventories excluding autos, which go into the calculation of GDP, rose 0.2 percent in June after a 0.3 percent gain in May.

An outright drop in inventory investment cut almost 1.2 percentage points from GDP growth in the second quarter, limiting the rise in output to an anemic 1.2 percent annual rate. Inventories have been a drag on GDP growth since the second quarter of 2015.

(Reporting by Lucia Mutikani; Editing by Paul Simao) ((Lucia.Mutikani@thomsonreuters.com; 1 202 898 8315; Reuters Messaging: lucia.mutikani.thomsonreuters.com@reuters.net)