Mr. Mubarak's problem

At first glance it would seem that a visit to the city of Jerusalem would be a small price to pay for the return to Egypt of the final third of the Sinai Peninsula.

President Hosni Mubarak of Egypt very much wants to get back that last slice of the territory which Egypt lost to Israel in the humiliating military defeat Egypt suffered in the ''six-day war'' in 1967.

But the price seems to get higher by the day.

The Israelis say he must not come to Israel at all unless he will include the city of Jerusalem in the visit. He has called off the Israeli plan for a four-day ceremonial visit including Jerusalem. In its place he has been willing to come for a one-day ''working visit,'' but not including the city of Jerusalem.

The visit was intitiated by Israeli Prime Minister Menachem Begin at the time of the Sadat funeral in Cairo in October. The idea was that the new Egyptian President would visit Israel before the scheduled final withdrawal of Israeli armed forces from the Sinai Peninsula. The visit would serve to underline the peace between the two countries which was signed at Camp David and which is supposed to continue after the final withdrawal of Israeli armed forces.

The withdrawal date is April 26.

The Israelis have all along expected that Camp David would mean continuing peace with Egypt and that following the withdrawal there would be a peaceful frontier between Egypt and Israel and freedom for normal trade and travel. They were willing to give up the whole Sinai Peninsula as their price to be paid for a safe and friendly frontier on their southern flank.

But they have become suspicious of late that Egypt's new President is more interested in regaining a place of honor and respect in the Arab community than in his future relations with Israel. The suspicion has played into the hands of the right-wing members of Mr. Begin's coalition who oppose the final withdrawal. They would be delighted to have an excuse to call off that final withdrawal, thus keeping in their hands a wide strip of Sinai land as a continuing buffer between Israel and Egypt.

Has President Mubarak given them the excuse they have wanted?

To demand that he visit Jerusalem on his four-day state visit is asking a lot of the President of Egypt. His predecessor went to Jerusalem in a dramatic gesture which opened up the Camp David process. But Mr. Sadat is no hero in the Arab world or even in his own country. And he is no longer with us. In most Arab eyes he became a betrayer of the Arab cause against Israel. They disapprove of the peace he made with Israel. And it all began with his flight to Jerusalem.

Much more history lies behind the importance of whether Mr. Mubarak goes in person into the city of Jerusalem.

After World War II the nations of the world sat down to decide the political map of Palestine after the end of the British Mandate. They provided for a Jewish state largely along the coastal plain of Palestine. Tel Aviv was its biggest Jewish center. The Arabs were to have the predominately Arab-populated hill country surrounding Jerusalem on all sides. But Jerusalem itself was to be a separate political entity under international control.

That plan was torn up by the fighting which broke out between Arabs and Jews as the date approached for the British withdrawal. When the fighting ended the Jews had driven a wedge up from the coastal plain to Jerusalem, but short of the ancient walled city. They developed what is known now as West Jerusalem. They built their parliament (Knesset) in that community. They soon began to call it their capital.

On July 30, 1980, the Knesset, by formal vote of 69 to 15 annexed the old walled city and Arab East Jerusalem, both of which had been seized in the '67 war. The whole of Jerusalem was declared to be the capital of Israel.

On Aug. 20 the Security Council of the United Nations voted for removal of all foreign embassies from Jerusalem in protest. At that time 12 Latin American states and the Netherlands kept embassies in Jerusalem. The others had remained in Tel Aviv. The US Embassy has always been in Tel Aviv and still is. Those embassies in Jerusalem have since moved back to Tel Aviv. Israel's claim to sovereignty over Jerusalem is not recognized internationally.

If Mr. Mubarak visits Jerusalem, he will, by so doing, give a degree of substance to the Israeli claim which no one else grants. But if he refuses he may put into the hands of the radical Israelis the excuse they want to cancel the final withdrawal from the Sinai peninsula. And that would be the end of Camp David.

King Henry IV of France gained his crown by accepting the Roman Catholic religion. ''Paris,'' he said, ''is worth a mass.''

To Mr. Mubarak, the lost territories are worth a lot - but an actual visit to Jerusalem may be too much.