The current rules, external came into place following an outbreak of foot and mouth disease in parts of Europe, and were in line with similar moves in the UK and other Crown dependencies.
Deputy Hilary Jeune had asked if the embargo was due to be lifted and, if not, why not.
Responding, Luce made reference to a number of diseases currently circulating in Europe, including foot and mouth, lumpy skin disease and African swine fever.
None of these diseases are currently present in Jersey.
However, Luce said personal imports posed “a particular challenge for traceability”.
He also said: “We continue to monitor the disease situation… and constantly review the information and disease risk.
“The intention is to lift the restrictions once the epidemiological situation in Europe improves, which may lead to acceptable risk for Jersey livestock population.”
The UK government, which maintains its own ban, said it was necessary to “protect British farmers”, external.