The Government congratulated Mr Ahmed Korei on assuming the office of Palestinian Prime Minister and wished him every success.
But it also warned Mr Korei the so-called roadmap for peace offers the best hope of a settlement to the conflict in the Middle East.
The Minister for Foreign Affairs, Mr Cowen, described the resignation of previous prime minister Mr Mahmoud Abbas as a major setback to the peace process and he urged all parties involved to show the maximum restraint.
"It is extremely important that they should take no actions which would make a renewal of the ceasefire and a revival of the roadmap more difficult," Mr Cowen said.
The Government also warned the expulsion of Palestinian leader Mr Yasser Arafat could lead to a political breakdown and further outbreaks of violence.
Meanwhile, Mr Korei warned he would not take the peacemaking job if it meant being under the same "Israeli dictate" that doomed his predecessor to failure.
He said before meetings with foreign envoys that he could not succeed if Israel did not stop air strikes and raids to kill or capture Palestinian militants.
"I have told the Americans, Arabs, Russians . . . everybody, that this situation cannot continue. I will not be under the Israeli dictate - 'do this and don't do that'," he said.
He was referring to Israeli demands that the Palestinian Authority break up militant groups, a step Palestinian officials have said could trigger civil war as long as Israel maintains a crippling military grip on Palestinian areas.
"This I will not do. I will do things only in favour of my people, in favour of the peace process. I am honest and very serious about making peace," said Mr Korei.
Mr Korei, was the former Palestinian parliament speaker and a moderate who is seen as close to Arafat.
The previous Palestinian prime minister Mr Mahmoud Abbas resigned on Saturday, blaming mainly Israel's military actions in occupied territory for his inability to carry out Palestinian obligations in a US-backed "road map" peace plan.
Additional reporting by Reuters
