Federal banking officials yesterday formally concluded an agreement with the United Mine Workers of America to end the union's 30-year control over the National Bank of Washington.

The agreement follows extensive reports of improper influence and bad lending practices involving some of the top officers and directors of the city's oldest and third-largest bank.

Although the union will retain ownership of three-quarters of the bank's stock, it must surrender two-thirds of the seats it now controls on the bank's 25-member board of directors, according to the agreement signed yesterday by a majority of the current board. The union now controls all 25 seats.

The agreement represents the most drastic enforcement action that could be imposed on the majority stockholder of a national bank short of outright federal takeover or forced sale. It reflected a deep concern within the Office of the Comptroller of the Currency, which regulates national banks, that the union's influence was threatening the financial stability of the 171-year-old institution.

Even as they were signing the agreement, the directors satisified one requirement that they find a new chief executive for the bank who would be acceptable to federal overseers, Luther H. Hodges Jr., deputy secretary of commerce and former chairman of the North Carolina National Bank, signed a contract yesterday to become the bank's new chairman and top officer. Frederick M. Henschel will remain as bank president, reporting to Hodges.

Sam Church Jr., the president of the union, was not available for comment after the meeting, but the agreement was clearly a blow to Church's prestige in the union that acquired the bank in 1949 when the union was under the leadership of John L. Lewis.

A public announcement of the agreement was delayed until today because federal banking officials insisted that each provision be spelled out in detail in a press release.

The nine-page agreement includes the following provisions, according to sources familiar with the document:

Directors will be prevented from participating in the day-to-day operations of the bank.

Directors also will be required to write a new and stricter code of ethics and set up a committee of new, independent directors to monitor compliance.

The bank will be required to hire a new chief lending officer acceptable to federal officials. [Church fired the former executive vice president in charge of credit.]

The bank's managers will have to develop a plan to reduce the $53 million in criticized loans identified this summer by bank examiners. These are loans with real or potential weaknesses in collateral or means of repayment.

Federal banking officials will have veto authority over decisions to declare dividends to stockholders. [In the past, such dividends have been the union's most important source of income.]

The federal action comes in the midst of two federal investigations into questionable practices at the bank during a period of unprecedented union involvement in key lending and policy-making processes. It also follows a series of articles published in The Washington Post two weeks ago detailing conflicts of interest, unsound loan practices and abuses of authority that became commonplace at the bank while it was under domination of the union.

While is was apparent that the primary goal of U.S. officials was to remove the mine workers from majority influence at the bank, neither of the official investigations conducted thus far -- one by the bank's audit committee and the second by federal bank examiners -- directly criticized the union hierarchy for improper conduct, according to sources familiar with the reports. h

Recent newspaper articles, however, have pinpointed the participation by Church and hand-picked union representatives on the bank board in unsound loan practices and abuses of authority.

The federal action, expressed as it was in "articles of agreement," was a step short of the more severe "cease and desist" order, which would have been enforceable through the federal courts. The terms of the agreement, if adhered to, spell a serious loss of control, prestige and, possibly, income in the form of dividends for the union.

Comptroller of the Currency John G. Heimann was not available for comment. He was known to have been considering as recently as a week ago a much tougher requirement that the union place its 750,000 shares of NBW stock in a blind trust, leaving the union leadership without even minority representation at the bank.

With the recent resignation of theater chain president Marvin J. Goldman, there are eight vacancies in the NBW board of directors, all of which reportedly will be filled by independent directors. Written into the agreement is a tightly worded definition of "independent," which would eliminate from consideration anyone with direct or indirect ties to the mine workers.

Even those directors chosen by mine worker's officials could be rejected by U.S. banking officials, sources said.

Barnum L. Colton, 83, who was John L. Lewis' choice to run the newly acquired bank in 1949, said yesterday that the federal action was "a good step," given the record of abuse in recent years.

Colton added, however, that it was the multimillion dollar deposits of the mine workers that enabled the National Bank of Washington to become, over the years, one of the city's largest.