Federal Judge Edward T. Gignoux today gave the Justice Department until June 1 to decide how it will proceed with claims by two Indian tribes to millions of acres in Maine.

Today had been the deadline for the department to tell the court how it would handle claims to land which the Passamoqueddy and Penobscot tribes say was taken from them two centuries ago in violation of an act of Congress.

The department outlined to the court Monday a plan for President Carter to appoint a mediator to help resolve the dispute. It said three months would be needed to negotiate such a settlement.

Involved was a reduced claim to about 5 million acres of land in Maine. The tribes said in a statement Monday that 3 million acres more could be included after a forthcoming departmental review. Claims to about 2 million acres of primarily coastal land, which is heavily populated, have been dropped for the time being, the tribes said.

Meanwhile, in Washington Maine's congressional delegation began its legislative fight to prevent the two tribes from suing to reclaim the land but to allow suits for monetary damages. A bill was filed in the House by Rep. William Cohen (R-Maine) and a similar one was introduced in the Senate by Sens. William D. Hathaway and Edmond S. Muskie, both Democrats.

Cohen, one of two House members from Maine, warned that Maine may try to hold the state of Massachusetts liable for any monetary damages his state may be required to pay the Indian tribes.

Maine was a part of Massachusetts in 1790 when the Peneobscots and Passamoquoddies signed a treaty with Massachusetts giving up title to the land. But the treaty was never approved by Congress, a requirement under federal law at the time.

It is on this basis that the Indians are suing for return of the land. The federal government is supporting their scaled-down claim.