Tournament organisers have postponed this season's European Champions Cup and Challenge Cup semi-finals and finals.
But European Professional Club Rugby says it "remains committed" to completing both competitions.
The quarter-finals next month had already been postponed, but now the semis from May 1-3 and finals in Marseille on May 22-23 have followed suit.
In a statement, EPCR said: "In making the decision, the board is abiding by the official directives and recommendations of the relevant authorities in its territories to restrict the COVID-19 pandemic.
"In light of the earlier postponement of its quarter-final matches and with fixtures in Europe's professional league competitions currently suspended due to the public health crisis, EPCR believes it necessary to provide as much clarity as possible to all stakeholders regarding the knockout stages of its tournaments.
"To that end, EPCR is working with the leagues and unions to restructure a conclusion to its season as part of a wider rescheduling of the remainder of the season in Europe, with all contingencies underpinned by the requirement to protect the health and welfare of players, club staff, match officials, supporters and the wider rugby community.
"EPCR remains committed to completing the 2019/20 Heineken Champions Cup and Challenge Cup season, and it is planned to reschedule the quarter-final and semi-final matches, as well as the Marseille finals, in line with fixtures in the professional league competitions, subject to advice from government and local authorities.
"EPCR would like to thank Olympique de Marseille, the staff at the Orange Velodrome and all local and regional partners for their continuing collaboration.
"An update regarding the knockout stages of the Heineken Champions Cup and Challenge Cup will be communicated as soon as practicable."
Champions Cup holders Saracens are among the clubs still in contention for that trophy this season, but face a tough quarter-final against Leinster in Dublin.
Gallagher Premiership rivals Exeter and Northampton are due to meet at Sandy Park, with the last-eight completed by Toulouse hosting Ulster and Clermont Auvergne entertaining Racing 92.
The Challenge Cup, meanwhile, sees Toulon tackling Scarlets, Bristol meeting the Dragons, Leicester taking on Castres and Bordeaux-Begles meeting Edinburgh.