Cardinal Agostino Casaroli, the Vatican secretary of state, is in satisfactory condition after undergoing emergency surgery to remove an injured spleen after a fall in New York City, hospital officials said.

Casaroli's spleen was removed Thursday because of internal bleeding, but the injury was not life-threatening, said a spokeswoman for the Cabrini Medical Center. He is expected to leave the hospital in a week to 10 days, said a spokeswoman at the Vatican's permanent observer mission to the United Nations.

The cardinal was a guest at the Vatican Mission for the United Nation's 40th anniversary when he fell down several steps Wednesday inside the residence of Vatican U.N. Observer Archbishop Giovanni Cheli, the mission said.

"The hallway was dark, and his eminence was running late to say mass," a spokeswoman said. "He slipped down several steps and struck his forehead."

Casaroli was admitted to the hospital late Wednesday morning or early afternoon with a cut on his head that required two stitches to close, and was held for tests. When it was discovered he had ruptured his spleen, doctors decided to remove the organ.

The cardinal's condition will force him to cancel meetings with several world leaders in New York.

United Methodist bishops will consider the first draft of their pastoral letter on "The Nuclear Crisis and Pursuit of Peace" at their semi-annual meeting in Wichita, Kan., next month.

The draft, which has been mailed to the bishops but not made public, was written in close cooperation with the staff of the Center of Theology and Public Policy on the campus of Wesley Theological Seminary here.

After discussion by the leaders of the nation's second largest Protestant church, the document will be revised and submitted for final adoption at the bishops' spring meeting next year in Madison, N.J. The letter is ultimately intended to encourage study of the nuclear issue by church members.

In its first public financial report since Cardinal John J. O'Connor became its archbishop, the Roman Catholic Archdiocese of New York reported that it had $1.2 billion in assets in the fiscal year that ended Aug. 31.

Total revenues were $276.7 million and total expenditures were $256.2 million, leaving the archdiocese with a $20 million surplus. But the report noted that 158 of the 411 parishes in the 10 counties of the archdiocese operated at a deficit.

A family life center founded and operated by the Evangelical Lutheran Church of Frederick, Md., is the winner of the 1985 Guideposts Church Award.

The $5,000 grant is given each year by the inspirational monthly to an innovative program that extends the ministry of a church or synagogue. Guideposts was founded by Dr. Norman Vincent Peale.

The Family Life Center was begun in 1982 by pastor-emeritus Francis Reinberger. It offers educational programs on such topics as parenting, child development, marriage, aging and retirement, and has established support groups for mothers and stepparents and child-care programs.

Rabbi Joseph P. Weinberg has been elected senior rabbi of the Washington Hebrew Congregation, succeeding Rabbi Joshua Haberman, who will retire next June 30. Weinberg, who has been assistant rabbi since 1968, is active in a wide range of community concerns in the Washington area as well as Jewish communal concerns locally and nationally.

The Rev. Margaret G. Adams will be installed tomorrow at 5 p.m. as pastor of the Silver Spring Presbyterian Church, 580 University Blvd. East. Adams, who served as interim pastor of the church for one year after the retirement of the Rev. Tracy Boyer in January, 1984, was selected from a field of 250 candidates.

She is the second woman in the National Capital presbytery to be installed as sole pastor of a church.

The Rev. Barbara D. Henry, formerly assistant rector at the Church of St. Stephen and the Incarnation, is the new assistant rector at St. John's Episcopal Church in Georgetown.

Joseph Rauh, longtime civil rights activist, will be honored by the Jewish Community Council of Greater Washington at the group's annual meeting tomorrow night at 7:30 at the Washington Hebrew Congregation, Massachusetts Avenue at Macomb Street NW.