(Corrects 10-year yield levels in paragraph 6)

NEW YORK, Aug 15 (Reuters) - Foreigners sold U.S. Treasury bonds and notes for a third consecutive month in June, data from the U.S. Treasury department showed on Monday, with some analysts pointing to softening investor demand after years of strong buying.

Offshore investors sold $32.9 billion in U.S. Treasuries in June after selling $18.29 billion in May. That followed record outflow in April of $74.6 billion.

Foreign official institutions, which include central banks, sold $33.5 billion in U.S. government bonds, while private offshore investors bought $2.4 billion.

"If you look at U.S. Treasury auctions, there has been generally less demand from foreign central banks, compared to last year," said Kim Rupert, managing director for global fixed income at Action Economics in San Francisco.

"It's also possible that investors are taking profits on U.S. Treasury positions after strong gains," she added.

Yields on U.S. 10-year Treasury notes at the beginning of June were 1.8440 percent, and later hit a high of 1.8560 percent. By the end of the month, yields were at 1.492 percent.

China remained the largest foreign holder of U.S. government debt, with $1.241 trillion in June, down from $1.2440 trillion the previous month.

Japan, the No. 2 foreign U.S. Treasury debt holder, posted holdings of $1.148 trillion, up from $1.133 trillion in May.

U.S. stocks, meanwhile, posted outflows for a fifth straight month in June, amounting to $6.8 billion. The only month that produced foreign inflows in 2016 was in January, when investors bought $4.6 billion.

The data also showed foreigners sold $3.6 billion in long-term securities in June after buying $40.8 billion in May. Including shorter-dated securities, overseas investors sold $202.8 billion, after selling $11 billion in May.

(Reporting by Gertrude Chavez-Dreyfuss; Editing by David Gregorio and Dan Grebler)