It said that a joint management of calendars was needed to coordinate the end of the current season with the start of the new one “which may be partly impacted because of the overstretch.”
It also called on leagues around Europe to work together.
“Only an extraordinary coordinated effort of all competition organisers can help European football out of the crisis, recovering in full its core asset, the competitions,” it said.
It added: “Stopping competitions should really be the last resort after acknowledging that no calendar alternative would allow to conclude the season.
“We are confident that football can restart in the months to come – with conditions that will be dictated by public authorities – and believe that any decision of abandoning domestic competitions is, at this stage, premature and not justified.”
It appeared to suggest that, where competitions did not end on the field, the clubs involved might not qualify for European competition next season.
“Since participation in Uefa club competitions is determined by the sporting result achieved at the end of a full domestic competition, a premature termination would cast doubts about the fulfilment of such condition,” it said.
It added that Uefa reserves the right to “assess the entitlement of clubs” to take part in the Champions League and Europa League.