By Balazs Koranyi

FRANKFURT (Reuters) - Britain's vote to leave the EU could be significantly negative for the euro zone, dampening a growth outlook that is already facing headwinds, the European Central Bank said in the minutes of its June 2 meeting, held before the British referendum.

The policymakers concluded that growth was being hurt by a weak external environment, particularly in emerging markets, and continued deleveraging by euro zone companies, and that risks remained tilted to the downside, requiring heightened attention.

Still, taking a cautious tone much like the U.S. Federal Reserve a day earlier, the ECB said time would be needed to see the full effect of its already unveiled but not yet implemented policy easing measures, particularly its corporate bond buys and a fresh round of cheap loans.

In the minutes of its own June meeting, the Fed said it would keep interest rates firmly on hold until it got a handle on the consequences of Britain's vote to leave the EU.

The ECB's minutes said that if Britain voted "Leave", "there could be significant, although difficult to anticipate, negative spillovers to the euro area via a number of channels, including trade and the financial markets".

The result of the June 23 referendum sent some markets into tailspin, boosting the euro - a negative for the ECB - but also lowering many sovereign yields, a positive for monetary policy.

ECB President Mario Draghi has said Britain's departure will lower euro zone growth by up to half a percentage point in total over the next three years.

Repeating an ECB pledge to take action if necessary, the policymakers agreed the bank would act with all tools available within its mandate if the inflation outlook required.

For the ECB, one of the most pressing issues may be the investor flight to top-rated government debt seen since the referendum, which reduces the availability of bonds to purchase as part of its 1.74 trillion euro quantitative easing scheme.

Nearly a third of euro zone government bonds are no longer eligible for the asset buying scheme because they yield less than the bank's minus 0.4 percent deposit rate, according to Tradeweb data on Thursday.

The ECB said a remark had been made at the June meeting that markets see a future challenge in sourcing sufficient volumes of debt to buy, possibly leading to increased price volatility.

Although the ECB can substitute assets if it cannot buy enough government debt, investors remain closely tied to specific market segments, so the actual composition of purchases still matters, the ECB added.

Some analysts predict the bank will not have enough German, Irish and Portuguese bonds to buy due to its self-imposed limits, forcing the ECB to tweak some of its rules if it wants to maintain monthly purchases at 80 billion euros per month until March, when the scheme is due to run out.

Any extension of the purchase program, expected by many analysts and investors, would almost certainly require changes either in the self-imposed limits or the types of assets the bank can buy.

(Reporting by Balazs Koranyi; Editing by Kevin Liffey)