Measures were introduced by Agriculture, Fisheries and Food Minister Mary Coughlan last month, suspending the importation of certain cattle and sheep from bluetongue-restricted zones.
Similar action was taken by her Belfast counterpart, Michelle Gildernew, to bring the North into line with the south.
But the Irish Farmers Association and the Ulster Farmers Union want the importation of all susceptible animals, which have resided in bluetongue-restricted zones since August 1, 2006, suspended until transmission routes for the disease are clarified.
The adequacy of existing EU Commission conditions under which live animals are allowed to be moved from such zones has been opposed by Ms Coughlan.
Draft proposals prepared by the commission will be discussed at a meeting of the Standing Committee on the Food Chain and Animal Health in Brussels on March 31.
Meanwhile, farmers here are advised not to import livestock under any circumstances.
A joint delegation from the IFA and UFU led by their respective presidents, Padraig Walshe and Kenenth Sharkey, outlined the need for a tighter import ban at a meeting with Ms Coughlan in Dublin this week.
IFA deputy president Derek Deane said Ms Coughlan agreed to pursue the suspension of imports through a significant tightening of the EU trade regulation at commission level.