Foot-and-mouth restrictions are expected to be eased today, after the Government's expert group on the disease met yesterday to issue recommendations to the Minister for Agriculture.
Mr Walsh said he would be making decisions today, based on recommendations from the group.
Meanwhile, trade restrictions inside the Co Louth foot-and-mouth surveillance zone have been lifted by the European Commission, which is satisfied the area is disease-free, the Department of Agriculture said.
Restrictions still applied inside the 10 km surveillance zone despite restrictions being lifted elsewhere on April 19th, when the State was officially declared free of foot-and-mouth.
Meanwhile, the Minister for Justice, Mr O'Donoghue, said there would be further prosecutions for livestock-smuggling.
Department vets had continued to take samples from cattle and sheep in the surveillance zone surrounding Proleek, Co Louth, the site of the State's sole confirmed outbreak of the disease.
The test results, which were received by the Department yesterday, all proved negative, a spokesman said. A spokesman for the Department of Agriculture said the Commission was satisfied there was no residual infection in the area.
Results are expected today from tests on samples taken from a sheep which showed symptoms of the disease, near Dunleer, Co Louth, outside the surveillance zone.
A Department spokesman said the results had been expected yesterday, but would probably arrive today. Sending them for tests to the Pirbright laboratory in Surrey was only precautionary, he said.
Other test results, from samples of three sheep in Co Cork, may be due today or tomorrow, he said.
Samples from the three ewes on a farm near Watergrasshill, Co Cork, were sent to Pirbright on Friday. But the Department has described the tests as purely precautionary.
The Minister said if the State remained free from foot-and-mouth by the end of this week, "a great deal" of normality would return. The State would move from a situation of foot-and-mouth containment to prevention.
He was speaking as he undertook a joint inspection yesterday of checkpoints in the Border area with the Minister for Justice.
Mr Walsh said it was difficult to say how long the checkpoints would remain in place.
"We have to get through this week. It is a vital week. If we get to this weekend, then we will, hopefully, allow a great deal of normality to recommence again," Mr Walsh told RTE.
Farming organisations last week met the expert group to discuss protocols to facilitate safe animal movement.
The Minister said: "The farming community are coming under a good deal of pressure now, because the grass was late this year - it was a late spring - and they want to move cattle to new pastures".
Fine Gael's agriculture spokesman, Mr Alan Dukes TD, called for "a realistic and public risk assessment of the resumption of livestock movement between farms".
The greatest problems facing livestock farmers was that they had far more stock than they would normally carry. Fodder was the main problem, with acute shortages in many cases.