FRANKFURT, July 9 (Reuters) - European Central Bank policymakers debated a cut in stimulus at their June 10 meeting as the recovery picked up pace but eventually found "broad agreement" to maintain an elevated level of support, the accounts of the meeting showed on Friday. Facing rising borrowing costs amid a still-fledgling recovery, ECB policymakers concluded that an early retreat from the market could push yields higher and choke off growth as some key sectors were not yet on a solid enough footing, even if growth was now relatively quick. But that conclusion was only made after conservative policymakers made a push to reduce the pace of bond purchases so ECB policy would stay in sync with improving real economic indicators. "In view of the better outlook for growth and inflation, and the associated upside risks, it was ... also argued that, to provide the same degree of accommodation, asset purchases should be scaled back somewhat," the ECB said. Ultimately however, financing conditions were assessed as "too fragile" to allow a meaningful reduction in the pace of purchases without risking a disorderly rise in yields, the ECB added. "It was stressed that the recovery was at an early stage and lacked robustness, as it depended heavily on policy support," the ECB said. "A noticeable slowing of the pace of purchases for the next quarter was therefore seen as inappropriate at the current juncture." In fact, some policymakers even argued that given a muted inflation outlook over the medium term, even an increase in stimulus could be justified. Commentary from the June meeting may not provide firm guidance about the bank"s next policy move as a new strategy, unveiled on Thursday, is likely to be the primary guiding force for decisions as early as the ECB"s July 22 meeting. read more The new strategy set the bank"s inflation target at 2%, giving up its previous formulation of "below but close to 2%" and signalled that periods of low inflation, as currently experienced, may require more persistent monetary policy action. While ECB President Christine Lagarde did not fully explain what this would mean in practice, sources close to the discussion said the bank is contemplating a new policy guidance for the July 22 meeting that would signal an even longer period of policy accommodation. read more While there was unanimous support for the eventual policy decision in June, several conservative policymakers argued at meeting for somewhat lower bond purchases under the ECB"s 1.85 trillion euro Pandemic Emergency Purchase Programme. Reporting by Balazs Koranyi; Editing by Catherine Evans and Andrew Heavens Our Standards: The Thomson Reuters Trust Principles.