All mayors of old cities face the tough problem of reconciling respect for history with the imperatives of modernization. Teddy Kollek of Jerusalem also must try to make his city indivisible.

Jerusalem was divided with barbed wire and land mines from 1948, when Jordan's Arab Legion seized the Old City, to 1967, when the Israeli army reconquered it. The Arabs never recognized the reunification.

Kollek is not the only one haunted by the specter of another partition or internatinal control. The specter has become particularly ominous since last summer when the Knesset, Israel's parliament, passed a "Jerusalem law" which reiterated that Israel considers the holy city its capital.

Kollek called this gesture "useless and provocative." The Arab nations, meeting in Saudi Arabia some days ago, restated their resolve to wage holy war.

The tension, exacerbating the intense emotional interests of Jews, Moslems and Christians, makes every aspect of city planning in Jerusalem a matter of worldwide interest. Kolleck, a somewhat disheveled looking, blunt bundle of energy, who has been called "the world's only statesman who operates out of city hall," knows it.

As soon as the reconstruction of the reunited Jerusalem began in the late 1960s, he invited an international committee of architects, urban designers, historians, theologians, legal experts and economists to look over his shoulder, so to speak, and advise him on matters of historic preservation, esthetics, cultural and social planning. "The world should have a say in what we do," he said.

Kollek's Jerusalem Committee is no public relations gimmick. Kolleck sincerely wants advice, not merely endorsement. Surprised but gracious, he reversed himself when the committee's architects knocked down the city's early and eager urban renewal, highrise and freeway proposals. In the nick of time Jerusalem was saved from Los Angelization.

Last week, some 25 U.S. and Canadian members of the committee met at the University of Notre Dame at the invitation of its president, the Rev. Theodore M. Hesburgh. The purpose of the meeting was to review progress and recommend policies for the continued tranquility of Jerusalem amidst tension and terror in the Middle East. The threat of partition was much on everyone's mind.

J. Kenneth Blackwell, the former mayor of Cincinnati and a black, called partition "Solomon's solution: cut the child in half.

"Internationalizing Jerusalem," Blackwell said, "also has superficial appeal. Instead of cutting the baby in pieces, we will place it in a foster home.

"This approach might be more attractive to me if I could be convinced that the prospective foster parents knew the first thing about child care.

"The best way to make Jerusalem a safe and attractive place for a cosmopolitan, multi-cultural, socio-economically diverse population to live and worship in and to attract tourist business, is the undisputed sovereignty of one nation.

"Under the Jordanians," the former mayor said, "all of the Old City's 27 synagogues were demolished. Torah scrolls were burned or stolen. Tombstones were used as building blocks for latrines.

"But I will acknowledge that the Jordanians were equal-opportunity despoilers. Under their care, Moslem shrines also suffered years of neglect, if not active destruction.

"Luckily, one of Jerusalem's historical parents is alive and well," Blackwell added. "The natural parent -- Israel."

Blackwell, who had visited Jerusalem to attend last April's conference of American mayors there, was obviously impressed. Despite continuing terrorist pressures, he told the meeting, "strong civic leadership has refurbished and reconstructed holy places of all faiths, and encouraged construction of new health care, educational, recreational and business facilities, as well as new mosques and churches and synagogues.It has installed modern water, drainage, electrical and telephone lines. And it has assured access of visitors of all faiths to the places they judge holy."

Jerusalem has almost doubled in size in the 13 years since it has been reunited, but it is still a small city considering all the passions it engenders. Of the 430,000 total population, 300,000 are Jews, 115,000 are Arabs (100,000 Moslem) and 15,000 are Christian. But that is just a very rough summary of the multitude of religious and ethnic divisions. Some ultra-orthodox Jewish sects, for instance, like to spend their Saturdays throwing rocks at less orthodox Jews who violate the Sabbath by driving their cars on Ramot Road. The Christians in the Old City are mostly Armenians. In new Jerusalem, Christians come in a variety of sectarian shadings of Roman Catholic, Greek Orthodox and Protestant.

There seems to be general agreement, at least within Jerusalem, that everyone's worship is unhampered and that the holy places are well taken care of by their respective denominations.

Kollek's overall planning policy is to make the old walled city the glorious jewel it ought to be, but to make it a living jewel, teeming, as it has for thousands of years, with day-to-day life.

The setting for the jewel is to be a greenbelt around the old wall, surrounded by the modern city, built in a spirit of diversity within a basic harmony. Even in the age of computers, Jerusalem must remain the city that was King David's caital, where Jesus was crucified and from which Mohammed rose to heaven on his black steed.

The incomparable "architect" of this harmony is the famous "Jerusalem Stone," a golden limestone with which the entire Old City was built and which, by virtue of a law passed under British rule, is the mandatory exterior building material for all new construction as well.

Many of Kollek's advisers hope that a new city, too, will eventually be surrounded by a greenbelt, a ribbon of open space that makes clear where the city ends and the country begins. There is already a tendency toward messy urban sprawl.

Reconstruction of the Jewish Quarter within the walled city, which was all but demolished in the 1948 War, is virtually complete. Television antennae have been replaced by underground cables. The Arab Quarter still needs a lot of modernization, particularly of what planners call "the infra-structure" -- sewers, water mains, telephone lines, etc.The water consumption in the Arab Quarter, to cite just one example, has increased 10 times since reunification.

The wall has been largely repaired and cleared of fanciful additions and lean-to-shacks that do not belong.

A project that will help modern life in the old city is "Jerusalem Rova," designed by the San Francisco landscape architect Lawrence Halprin. It provides for a discreet car entrance via a tunnel under the Turkish Tower, a solution that proved esthetically far superior to widening the ancient gate.

There also is to be underground parking and an underground bus terminal. Halprin hopes to introduce elctric carts to service the Old City. The tranportation structures are to be hidden by houses, shops and restaurants, and integrated with the Old City by a system of terraces and walkways.

An important feature of Halprin's project is an archeological garden, a sort of landscaped excavation site, which preserves and provides access to ancient ruins of Biblical times.

There are to be no more highrise buildings. The few that were built in recent years are ugly enough.

The predominant problem in the new city is housing. Oddly enough, the economically poor Arab houses and shacks in East Jerusalem are esthetically far more pleasing and in keeping with Jerusalem's character than the modern housing blocks built for the Jews by the state of Israel. Arabs, understandably, will not live in these Bauhaus barracks. For other reasons, too, the two life styles cannot be integrated and nobody in Jerusalem is trying to.

The policy is rather to make the city "a mosaic of homogeneous neighborhoods."

"We want Arabs in Jerusalem to enjoy the same cultural and political freedom we expect Jews to be granted in Syria, say, or in the Soviet Union," Kollek said.

Existing neighborhoods, or "urban villages," are being strengthened and new ones built. The Notre Dame conference also recommended giving these ethnic neighborhoods self-government in such matters as education, municipal services and administrative practices.

Common meeting grounds are also intended to forge the city's unity.

Traditionally the meeting grounds of Jews, Arabs and Christians have been the bazaars in the Old City. The different denominations shop and dine and such in one another's business centers as well as their own. Jerusalem's new downtown shopping center, the most ambitious current project, is carefully located to foster this interaction.

The site is a former slum along Mamilla Road, close to the Jaffa Gate, which was no-man's land under Jordanian rule. The architect is Moshe Safdie, who rose to fame with his Habitat '67 project at Montreal and Coldsprings, the new town in Baltimore. He now is heading the urban design department at Harvard.

In the course of several years of controversy, the project has been considerably revised and scaled down. It is now, in Safdie's words, to be a "thriving bridge" not only between the old and the new city but also among several neighborhoods. There will be shops, offices, housing, a public plaza, a large pool and a parking garage hidden by hanging gardens.

Independently, Safdie's Harvard students received a three-year grant to study Jerusalem and prepare urban design plans for the city.

Kollek is also doing as much as public funds and private donations permit to build up parks, libraries -- an entire new cultural complex -- which all Jerusalem residents will be able to use and enjoy. He wants his city to be "a flourishing center for learning and culture."