* Payrolls figures key for start of next quarter * Bond funds have seen huge outflows * Fed officials continue to try to soothe markets By Luciana Lopez NEW YORK, June 28 (Reuters) - The prices of benchmark U.S. Treasuries fell in choppy trading on Friday, capping a week when prices began to stabilize after yields shot to a near two-year high on a recent Fed-induced selloff. With month- and quarter-end activity adding to volatility, Treasuries looked set to close out their worst quarter since the start of 2012. Coming sessions could stay choppy, too, said Justin Lederer, strategist at Cantor Fitzgerald in New York, especially going into next Friday's payrolls report. "That could definitely set the tone for a date for QE," he added, referring to the timing of the Fed's potential pullback from its bond-buying program, known as quantitative easing. "I wouldn't be surprised if we tried to touch the high yields again, but it's just dependent on data and what goes on around the world," Lederer said. The quarter proved a challenging one for Treasuries. The slump in prices started in May, gaining momentum when Fed Chairman Ben Bernanke suggested that the bank could be looking for an exit from QE. But the magnitude of the selloff became a stampede last week, when Bernanke said more emphatically that the Fed could begin slowing its $85 billion per month of bond purchases this year as the economy improves. The iShares Barclays 20-year-plus exchange-traded fund , one of the most popular bond ETFs, is on track for a loss of about 7.24 percent for the quarter, its worst drop since the first quarter of 2012. However, Fed officials speaking this week have taken pains to reassure investors that the U.S. central bank will not halt all its stimulus measures at once, with policymakers not yet ready to raise interest rates for months or even years yet. Among the latest voices in the Fed chorus was Governor Jeremy Stein, who said the bank must consider overall economic improvements since it launched the stimulus and not give undue weight to the most recent economic data. A longer view is needed for the Fed's policy-setting committee to make a good judgment and to avoid undue market volatility, Stein said, according to prepared remarks for delivery to the Council of Foreign Relations. Jeffrey Lacker, the president of the Federal Reserve Bank of Richmond, also spoke on Friday, pointing out that markets should brace for more volatility as investors weigh news that the central bank will pull back bond buying later this year. This is a normal adjustment and should not derail growth, he added. The benchmark 10-year U.S. Treasury note's yield has backed away from the 22-month high of 2.67 percent reached on Monday. On Friday, the 10-year note fell 9/32 in price to yield 2.508 percent, compared with 2.4758 percent late on Thursday. Even so, the yield remains significantly higher than the 2.20 percent area it traded at before Bernanke's comments last week, and above 1.60 percent at the beginning of May. Bond funds have struggled in recent weeks. Investors in funds based in the United States pulled $8.62 billion out of taxable bond funds in the latest week, marking the first four-week streak of outflows from the funds since 2008, data from Thomson Reuters' Lipper service showed on Thursday. But some analysts said the Fed might find it harder than markets realize to slow its purchases of Treasuries and mortgage-backed securities. The Fed plans to pull back "only if the U.S. economy offers a combination of lower unemployment, faster growth and stable inflation," wrote HSBC Economists Stephen King and Madhur Jha in a report. "The Fed's own forecasts suggest this holy trinity may now be within reach. Our forecasts suggest otherwise." As if to underscore that point, the Chicago Purchasing Management Index fell to 51.6 points in June, lower than the 56.0 economists had forecast and below the 58.7 in May. "Over the past three to four months, a variety of economic indicators have suggested that the economy lost momentum at the end of Q1 and beginning of Q2," said Thomas Simons, money market economist at Jefferies & Co in New York. "We are optimistic about a recovery in the manufacturing sector in the second half of the year, but the path to growth will not be free of bumps," he said. The government's payrolls data for the month of June, set for release next Friday, will be closely watched by investors. The release comes one day after the U.S. Independence Day holiday, which may reduce volumes and make trading on the number more volatile. As part of its stimulus efforts, the Fed on Friday bought $1.46 billion of Treasuries maturing between February 2036 and November 2042.