VATICAN CITY — Negotiations over the Vatican’s adherence to international banking standards were reaching a delicate point. During a lunch, a European official later recalled, discussion turned to the need for more openness from an institution steeped in centuries of secrecy.

A Vatican representative at the meal, annoyed by the requests for more information, shouted, “How can you ask us such questions?”

The clash came amid mounting pressure on the Vatican to clean up its bank — for decades the subject of dark intrigue and linked to one mysterious death — as part of a push by the European Union to apply common rules to all the countries and micro-states like Vatican City and Monaco that use the euro.

Those pressures continued until the very last days of Pope Benedict XVI’s papacy and remain a critical issue for the cardinals now meeting to elect a new pope. As the conclave begins Tuesday, the specter of financial scandal presents a special challenge for Benedict’s successor, who must modernize the Roman Catholic Church’s finances or risk the Vatican’s access to the global banking system, undermining its moral authority and its financial stability.