About 300 settlers who erected an illegal encampment near this West Bank site, hoping to force the government to start building a new Jewish community before the forthcoming national elections, rejected appeals tonight by Prime Minister Menachem Begin's office to move.

Spokesmen for the squatters, who have erected a concrete block building and tents, said they would not leave because the government three years ago designated the site for permanent housing for a settlement. They said if work does not begin now, a new Labor Party government might scrap the plans.

The issue, however, already has turned into a political struggle in Begin's Cabinet, with Agriculture Minister Ariel Sharon and Housing Minister David Levy, rivals for leadership in Begin's Likud bloc, refusing to yield to compromise proposals.

Levy condemned the ultranationalist settlers as "illegal squatters who are trespassing on land that is not theirs," and insisted they be removed. Sharon, architect of a government program to rush construction of new West Bank settlements before elections, warned that by driving away the settlers, the government would be "doing the Labor Party's job."

[The Reagan administration today criticized Israel's decision to continue building new settlements in the occupied territories, saying it is not "helpful."]

The dispute caused the breakup of a meeting of Likud Cabinet ministers called to discuss unity and it threatens to widen divisions within the government even before the election campaign. Parliament is expected to schedule elections for June 23.

Begin today sent his director-general, Mattiyahu Shmuelevitz, to meet with the settlers.