A group of Mobil Oil Corp. stockholders yesterday asked Mobil's board of directors to investigate allegations of mismanagement by the oil company's president.

The request was made in a letter, which the stockholders said was the first step toward a lawsuit should Mobil's directors deny the request.

The letter was delivered yesterday to Mobil officials by the Washington law firm of Lobel, Novins & Lamont, which represents the stockholders. The stockholders said they want their request on the agenda of Mobil's board of directors meeting Friday.

The letter followed Washington Post articles detailing the role of Mobil president William P. Tavoulareas in setting up his then 24-year-old son in a shipping management firm that has done millions of dollars in business operating Mobil-owned ships.

The stockholders were identified as the Province of St. Joseph of the Capuchin Order, a Detroit-based order of Roman Catholic priests, and Edwin Rothschild, whose 2-year-old son, Andrew, owns one share of Mobil stock.

The elder Rothschild is the director of Energy Action, the Washington based public interest energy group. A spokesman for the Capuchins, Rev. Michael H. Crosby, said the 12,000 member order owns 2,000 shares of Mobil stock.

In a two-paragraph statement, a Mobil spokesman responded to the letter by saying, "Mr. Lobel's letter is filled with innuendo and unsubstantiated statements. The points he makes have been fully and publicly disclaimed by Mobil and his letter will be answered in due course."

Mobil also accused Energy Action of having "a long history of abusing facts to attack oil companies,"