ALBANY – As the seriousness of Governor Pataki’s medical condition becomes more evident, political life and the basic functions of government appear to be humming along.

Already a diminished presence in the state Capitol, Mr. Pataki will soon be entering his third week of hospitalization, an absence that is reinforcing his status as a lame-duck executive.

While doctors treating Mr. Pataki say he is showing signs of improvement, they gave no word of when he might be released from New York-Presbyterian Hospital/Columbia Medical Center, where he is suffering from peritonitis, a potentially life-threatening infection that he developed after undergoing an emergency appendectomy. The governor has a badly infected digestive system, and it could be days or weeks before he returns to his executive chambers.

Yesterday, lawmakers insisted there was no rush. At a press conference, the Republican Senate majority leader, Joseph Bruno, said Mr. Pataki’s absence hasn’t affected budget negotiations. With a month before the budget is due, Senate and Assembly leaders are busy negotiating how much spending and taxing they want for the next fiscal year.

Mr. Bruno said he talked with the governor on Monday and told him: “You ought to stay there as long as you have to stay, and don’t feel pressure in any way.” The senator, with a bit of a grin, then looked at a reporter sitting down in front of him and asked, “What are you laughing at?”

Top officials in Mr. Pataki’s office say the governor essentially has transferred his office to the hospital bed and is eager to be released. Speaking to reporters, Mr. Pataki’s chief of staff, John Cahill, joked that the governor is so intent on working a full day that Mr. Cahill has to pull away the governor’s BlackBerry. “His energy level is very good,” Mr. Cahill said. “He’s fully engaged in all of the issues.”

Doctors disclosed for the first time that Mr. Pataki was suffering from peritonitis, an infection that involves the inflammation of the lining of the abdominal cavity and is often caused by a ruptured appendix. The symptoms of peritonitis include severe abdominal pain, nausea and vomiting, fever, abdominal distention, and fluid in the abdomen, according to the Web site of New York-Presbyterian Hospital. If not treated immediately, it can be fatal; both Harry Houdini and gangster Dutch Schultz died from the infection.

Doctors are treating Mr. Pataki with intravenous nutrition and antibiotics and said he wouldn’t be released until his fever goes away and the bowel obstruction in his digestive system is “resolved.” They said they expect the governor to return to “complete normalcy.”

The most serious result of Mr. Pataki’s illness could be on the governor’s political future. His medical problems have taken him out of the action at a point when he is seeking to build a national reputation and present himself as a viable 2008 presidential contender. Mr. Pataki’s condition could prevent him from making trips to Iowa and New Hampshire, the locations of the first presidential caucuses and primaries, for weeks or months. This past week, Mr. Pataki missed a Republican fundraiser in Rochester, as well as this year’s meeting of the governors association and the New York State Conference of Mayors’ gathering in Albany, which Senator Clinton attended.

A year ago at this time, Mr. Pataki was in Washington, asking the Pentagon not to close any bases in New York and attending a meeting of the National Governors Association. He also announced during the same period that he was asking his tax department to draft new regulations on collecting taxes from Indian reservations.

Hank Sheinkopf, a veteran Democratic political consultant and a spokesman for state attorney general candidate Mark Green, said Mr. Pataki’s absence “doesn’t have a lot of impact on anything. He’s not really there anyway.”