A high-level Arab delegation headed by Morocco's King Hassan II arrived here yesterday for discussions with President Reagan on Friday about his peace initiative for the region.

Arriving at Andrews Air Force Base, Hassan noted that "we are realists and we know we cannot in a few days or a few months find solutions for a problem which is 40 years old."

In another development, Secretary of State George P. Shultz will meet with Israeli Foreign Minister Yitzhak Shamir for the third time in a week to review the problems impeding an agreement on the withdrawal of Israeli and other foreign forces from Lebanon.

The two sets of meetings involve what U.S. officials call "the separate but parallel tracks" that the administration is pursuing in hope of resolving what it regards as the two most urgent problems affecting the region: settlement of the Lebanon crisis and, beyond that, ending the Arab-Israeli conflict.

But despite the flurry of diplomatic activity -- which also included a meeting Tuesday between Reagan and Lebanon's new president, Amin Gemayel -- the prognosis among U.S. officials and other diplomatic observers is that many weeks, and probably months, will be required before there are any signs of even a tentative breakthrough on either problem.

Administration sources now concede that Shultz, who had hoped to capitalize on the momentum of Reagan's Sept. 1 speech outlining his initiative by going to the Middle East this fall, now believes there is no point in attempting such a journey until next year.

As State Department spokesman John Hughes said yesterday in response to questions about the purposes of the Arab delegation's visit, "It's one more step in a continuing process. It may seem lengthy and drawn out. But it's a complex process and it's going to take time."

In addition to Hassan, the Arab delegation is expected to include representatives of Syria, Saudi Arabia, Jordan, Tunisia and Algeria.

Its aim is to explain to Reagan the stance the Arab League adopted last month in Fez, Morocco, calling for Israeli withdrawal from occupied Arab territories and establishment of an independent Palestininian state in the West Bank and Gaza Strip under the leadership of the Palestine Liberation Organization.

On its face, the Fez declaration is a rejection of Reagan's initiative, which advocates eventual autonomy for the West Bank and Gaza "in association with Jordan."

However, U.S. officials have tended to regard the Fez declaration as an opening position for protracted diplomacy that eventually might move the Arab states closer to the U.S. position; and the administration is encouraged by one provision in the Fez statement implying an eventual Arab recognition of Israel's right to exist.

Shamir had been visiting Costa Rica and stopped in the United States for 24 hours en route home. Reliable sources said Shultz offered last week to have Reagan's special Lebanon negotiator, Morris Draper, meet Shamir in New York to brief the Israeli minister on Gemayel's visit, but it later was decided to have Shultz and Shamir talk directly.

The meetings with Shamir and Gemayel made clear that there is a gulf between Israel's proposals for a security zone in southern Lebanon that would leave the region effectively under Israeli control and Gemayel's preference for giving the job of policing such a zone to an expanded multinational force that probably would have to include U.S. troops.

Draper will return to the area over the weekend to make a new try at cutting through the differences, but there is growing pessimism in official U.S. circles about the chances of getting an agreement that will see foreign forces withdrawn from Lebanon by year's end.