President Carter yesterday reaffirmed the United States' policy of "impartiality" in the bloody conflict in Northern Ireland and called on the American people not to support organizations that are involved in the violence in that bitterly divided country.

In a mildly worded statement released by the White House, the President pledged the United States' "complete support" for efforts to establish "a peaceful and just society" in Northern Ireland. Once a peace settlement is reached, he said, the United States "would be prepared to join with others to see how additional job-creating investment could be encouraged, to the benefit of all the people of Northern Ireland."

White House press secretary Jody Powell refused to elaborate on the offer of investment aid, but said the statement did not refer to direct government assistance.

Carter's statement, believed to be the first time the explosive Northern Ireland issue has been addressed publicly by an American President, came after weeks of speculation in the British and Irish press about a supposed American peace initiative. Last week, however, Powell had warned reporters that such speculation was over-blown and that the United States could take only very limited steps toward encouraging a peace settlement.

The President's statement was initiated at the suggestion of several important Irish-American members of Congress, among them House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), Sen. Edward M. Kennedy (D-Mass.) and Sen. Daniel Patrick Moynihan (D-N.Y.).

O'Neill said yesterday that Carter "is the first American President to speak out and contribute in a positive way" toward ending the violence in Northern Ireland. Kennedy called the statement "the most important and constructive initiative ever taken by an American President on the Irish issue."

Carter's statement was particularly mild when contrasted with the administration's attempts to play a much more active role in seeking peace settlements in the Middle East and southern Africa.

The President said the United States supports the establishment of a form of government in Northern Ireland that would command the acceptance of the country's Protestant majority and Roman Catholic minority. But he warned that "the only permanent solution will come from the people who live there. There are no solutions that outsiders can impose."