Federal Reserve policymakers last month saw signs that the economy was healing after its winter slump but still wanted more signs of improvement before they began raising interest rates.
Minutes of the June 16-17 discussions showed that while one Fed official was ready to begin raising rates at that meeting, "most participants" believed that conditions were not yet ripe for a rate increase.
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The minutes revealed that many Fed officials expressed concern about the impact a failure to get a deal on Greek debt might have on financial markets.
While private economists had expected the Fed's first rate hike to occur in September, the standoff on Greek debt and the sharp plunge in Chinese stock prices have prompted many analysts to expect a delay until the end of the year.