The House plenum on Wednesday postponed a vote on amending the law on animal welfare to allow kosher slaughter until next week.
The postponement followed a request of Disy, Akel and the Greens.
The decision to allow the particular method until the end of the year was made to bail out animal breeders who have seen business fall as a result of measures against coronavirus by opening up alternative markets.
Animal welfare organisations have been against this move.
Green party chairman Giorgos Perdikis and MP Charalambos Theopemptou said in a letter to House President Demetris Syllouris that adopting such slaughter methods has not been demanded by any Cypriot religious group.
The Animal Party too said they struggled and will continue to struggle to stop the amendment of the law in question to allow slaughter of animals without anaesthesia.
The party said they reached out to President Nicos Anastasiades, contacted the agriculture minister and all political leaders in addition to Dutch MEP Anja Hazekamp, who is member of the Party for the Animals in her country.
Agriculture Minister Costas Kadis said earlier in the week that a clause inserted in the bill in question stipulates that animals will be anaesthetised right after their throats are cut to limit their suffering to the minimum.