Connecicut Gov. Ella Grasso, who have liver cancer, announced today that she is resigning at the end of the year because she lacks "the stamina or the endurance" to continue in office.

The first woman elected governor of a state in her own right, Grasso will be succeeded by Lt. Gov. William A. O'Neill, 50, a veteran of Democratic Party politics and a fiscal conservative. Grasso is in her second term as governor.

President Carter, who became a friend of Grasso, said she "has demonstrated and fulfilled the great potential of democratic government -- integrity, compassion and responsibiltiy" during her career.

Grasso battled cancer with characteristic spirit. She went home from the hospital Monday earlier than planned, saying she felt fine. Today she released a tape recording of her resignation statement, in which she sounded as if she were matter-of-factly announcing a matter of state business.

"If you called her right now and talked with her, you wouldn't know she was sick," an associate said.

But liver cancer, one of the gravest forms of the disease, is usually incurable, and the governor called state leaders to a morning meeting at her executive residence to announce her resignation.

They said they urged her to stay on, but she was adamant. State Senate President pro tempore Joseph J. Fauliso, who will become lieutenant governor, said Grasso was resigning because "she doesn't settle for anything less than excellence."

Grasso, who learned politics from the late Democratic state and national chairman John M. Bailey, was first elected governor in 1974. She attracted national attention as the first woman seeking a governorship without succeeding her husband, as other have, but her gender never became an issue in the campaign. This was in part because she had a reputation as "one of the boys in the Democratic Party."

During her first term, she ran into trouble as she laid off state workers to try to eliminate the multimillion-dollar state deficit. Critics said she kept appointing task forces rather than solving problems.

At the start of 1978 it was said she could not win reelection. But she capitalized on a major blizzard that closed roads in February 1978 to show her strength. She traveled everywhere by helicopter and residents showed their appreciation by stamping "Ella Help" messages in the snow. She easily won reelection and seemed in control and enjoying herself during the 1979 and 1980 legislative sessions.

But then she was operated on the April. Two weeks later it was announced she had ovarian cancer and that she had undergone a hysterectomy to try to remove the cancerous cells.

During her long convalescence, which included radiation treatments that made her nauseous and resulted in gastritis, Grasso continued to govern the state without interruption. Her illness did not seem to hamper her performance, and she had few major decisions to make.

However, a new legislative session starts Jan. 7 and Grasso said in her resignation today, "Regretfully, it is my belief that I do not have the stamina or the endurance for the rigors of the new legislative session."

In addition, she is a private person, and was uncomfortable at the extensive press coverage of her illness.

O'Neill, her successor, a former Democratic state chairman and past majority leader of the state House of Representatives, is considered a loyal Democrat with strong conservative beliefs. He is viewed as more of a technician than a man of vision.