Egyptian Foreign Minister Ismail Fahmi conferred with President Carter yesterday on their two nations' shared eagerness to thread a path through the obstacles to an Arab-Israeli peace conference.

"We are working on the question of Palestinian representation," Secretary of State Cyrus R. Vance told reporters as he and Fahmi left the White House to continue talks at the State Department.

Fahmi, agreeing, said Egypt has "constant contacts with the PLO [Palestine Liberation Organization], and we'll see how we can accommodate everybody."

To accomplish that goal will require something like the use of diplomatic mirrors. That is just about what the diplomats are trying to employ to overcome, or circumvent, the dispute over Palestinian participation in the conference.

Egypt's Fahmi is the first of a series of Arab foreign ministers to come to the White House after Israeli Foreign Minister Moshe Dayan. Fahmi will be followed in the next weeks by the foreign ministers of Syria, Jordan, Saudi Arabia and Lebanon.

All of the Arab nations are officially committed to the PLO as the "sole representative" of the Palestinians in the territory occupied by Israel in the 1967 Arab-Israeli war. Israel, in turn, is committed to reject an negotiations with the PLO, whose charter calls for dismantling the state of Israel.

The Carter administration is now trying to build on the added flexibility it claims Dayan displayed in his talks here.

Dayan publicly amplified the Israeli position on accepting some Palestinians from the Israeli-occupied West Bank of the Jordan RIver in a Jordanian delegation, saying they could be PLO "sympathizers," or representatives who are not on record as PLO members. U.S. officials said this delegation could include Arab mayors from the West Bank.

Administration officials said Dayan also agreed that Israel will consider reconvening a Geneva conference with a single, pan-Arab delegation. This is another device to help swallow-up the Palestinian dispute.

Fahmi yesterday spent an hour and 40 minutes at the White House, part of that time in private with the President. Fahmi said the talks "were positive" and he will meet again with Carter here or at the United Nations.

He told reporters he delivered a written message from President Sadat about the situation in the Middle East "and the role of the PLO in Geneva."

Before leaving Egypt, Fahmi said that "we cannot imagine the Geneva conference convening without the PLO being invited to attend on the same level as the other parties." Israel, however, has a written agreement with the United States that gives Israel veto rights on conference participants, and notably the PLO, unless it first acknowledges Israel's right to exist, which it has declined to do.

A statement issued after the talks with Fahmi said the President called for "compromise and courageous leadership" to produce a Geneva conference by the end of this year. This was the same language used after the talks with Dayan.

Unlike the statement issued after the Carter-Dayan talks, however, yesterday's made no reference to any "differences" between the two sides.

White House spokesmen were irked when reporters asked why there was no similar acknowledgment of differences with Egypt. Spokesman Jerrold Schecter said there was no need for the two statements to contain identical phraseology. He acknowledged that "we have differences on different questions" with Egypt.

Secretary Vance said the talks with Fahmi were "helpful and useful." Vance said there discussion also extended to the intensified fighting in southern Lebanon, where, Vance said, "It's terribly important" to prevent widened warfare and to achieve "a cease-fire immediately . . ."