Farmers will continue to block the Musgrave distribution centre in Kilcock, Co Kildare, until they get progress on their list of demands.
The group of farmers, known as the Individual Farmers of Ireland, began their protest on Sunday evening.
"We've put in our list of demands so we're waiting for replies back. Until we get some progress, there's definitely going to be no movement from here," a spokesperson for the group, who did not want to be named because of fear that legal injunctions would be used, told the Irish Farmers Journal on Monday morning.
One of their demands is that Green Party MEP Ciarán Cuffe resigns from his position over letters he sent to banks on farmer lending.
The Green Party distanced itself from Cuffe's comments on Sunday night. However, farmers at the protest are adamant he must go.
"Ciarán Cuffe has to go. There's no negotiation on that one, because what he did is just a huge attempt to close down farming in Ireland and he hasn't the right to do that. "
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"There is other things there [for] negotiation on, there's a list of demands gone into Government and until there's progress made, we would be looking at escalating at the other distribution centres."
No farmers, no food
"It's getting to the stage where you're not going to have farmers and if you've no farmers, you won't have food.
"Maybe we'll try a week with no food and see how people would like to try a week with no food. It's just getting too serious, there's no young farmers coming to the game.
"The main farm organisation of the country is not highlighting it enough, but when you've millionaires running those organisations they don't feel the pain," he said.
The spokesperson said that the list of demands has been given to Minister for Agriculture Charlie McConalogue.
"We're definitely not going home empty-handed and we're definitely not going home until we make progress, because it's just too serious.
"We have to put on massive pressure now."
When asked if they would join Monday's trucker and haulier protest in Dublin, the spokesperson said: "Let them do their job and we'll do ours".
"They've an issue with diesel, we've an issue with six or seven points, the Climate Bill being the main one. People haven't studied it enough."