Leon Cooperman and Steven Einhorn's Omega Advisors told investors the bull market in U.S. shares was intact and that equities should generate a mid-to-high single-digit annual total return despite August's market turmoil.

In a letter to investors dated Oct. 17 and seen by Reuters on Friday, Cooperman and Einhorn said it would take time to restore investor confidence in U.S. shares after the volatility and forced selling that drove stocks down 10 percent over five sessions near the end of August.

Omega said investor sentiment should improve if the market sees stability in Chinese economic data and in oil and commodity prices, a narrowing in corporate and high-yield spreads, clarity by the Federal Reserve on interest rates, rising U.S. Treasury yields and increased quantitative easing from the European Central Bank and Bank of Japan.

In a September letter, Cooperman and Einhorn blamed much of August's market turmoil on so-called risk parity funds and momentum investors known as CTAs.

In a separate interview with Reuters on Friday, Einhorn said: "These approaches to investing may have made those declines more severe. The message in September was not to blame somebody." Omega, which has $7.4 billion under management as of Sept. 30, closed August with a 6 percent loss.

"While U.S. shares have experienced a noteworthy correction, we do not believe the fundamentals that are relevant to the U.S. equity market have changed in any important way," Omega said. "If and as this becomes recognized, the U.S. equity bull market should resume."

Omega cited the Fed's gradual pace of tightening and attractive equity valuations as two of the "magnificent seven" items that will extend the bull run.

The others include: Economic expansion that will last for at least several more years; Real growth of between 2 percent and 3 percent; "Sweet spot" inflation between 1.5 percent and 2.5 percent; U.S. monetary policy that does not become hostile to risk assets or economic activity; market faces "wall of worry" sentiment.

Overall, Cooperman and Einhorn said eurozone and Japanese shares are attractive in an absolute sense relative to U.S. shares and relative to fixed-income alternatives.

"We entered the year 2015 believing the Japanese equity market (currency hedged) would outperform the U.S. and this has been the case," Omega said. "We continue with this conclusion based on the following: A BOJ open-ended and large QE program with the opportunity to increase in size; Double-digit earnings growth and attractive valuation."