Chicago Mayor Jane Byrne's sweep through the opening sessions ofthe 47th annual meeting of the United States Conference of Mayors this weekend has left her colleagues stunned, dismayed and, as one delegate put it, "Pretty damned jealous."

By all accounts, the first woman mayor of the nation's second-largest city upstaged her peers at every turn. Some examples:

In Saturdays opening addresses, Byrne turned what was supposed to have been a polite greeting to her fellow mayors into a lightning attack on President Carter's urban policies. Her colleagues were shocked, and some mumbled epithets.

Normally the mayor of the host city stars on the opening night of the conference. But, intentionally or not, Byrne snatched that honor from Pittsburgh mayor Richard S. Caliguiri Saturday night by throwing one of the most lavish parties ever witnessed bya mayors' convention.

Byrne brought along an entourage of at least 10 of her very visible and active city hall staffers. Several mayors, especially some from smaller cities, regarded her official following as an unnecessary show of force.

During her two-day stay here, Byrne was trailed by a horde of news people - 16 from Chicago alone. "You can't let that woman out of your sight. She throws out news stories like confetti," said Bob Crawford of CBS news in Chicago.

A flustered top aide to a major Mid-west city's mayor said: "She's obviously . . . well, I think . . . hell, Jane's just feeling her oats. But I don't want to be quoted."

Said a North Carolina mayor, who also requested anonymity: "No other city administrator could have come in here and gotten away with what she's gotten away with."

"Did you see the staff she brought?" And what about that party last night? She's something else."

Through it all, Byrne, 44, remained unperturbed.

"I don't pay very much attantion to the attention being given to me," she said in an interview before flying back to Chicago early this evening. "All of those cameras following me into the meeting this morning - I don't know why they were there. But I can't let that kind of thing interfere with what I have to do."

Byrne said she thought the media overreacted to her statements Saturday criticizing Carter.

"I did not say I would not endorse him. I even pointed out that I did not want any comments to be interpreted as being that I was offering lukewarm support. . . .

"I simply said that I don't think the current administration is answering to the needs of the cities."

On another issue, she acknowledged that Carter is "trailing very badly in the polls in Illinois. But he was doing that before I said anything.

"I think Carter has got to get his act together in dealing with the cities. I think he's got to get his staff together, too."

Asked to elaborate Byrne said "They're kind of shaky."

The mayor said she had something else she wanted to explain. She raised eyebrows Saturday by saying that the United States is experiencing an influx of illegal aliens and legal immigrants. "They're coming to the cities. . . . You can bet they're not coming to Plains, Georgia," she said.

Byrne said today that her comments were not meant to belittle Carter's home town, nor were they meant to disparage rural America.

Immigration, legal or otherwise, primarily affects the nation's larger cities, Byrne said. "What I was trying to say is that you can't really expect people from Plains, Georgia, to understand big-city problems," she said.

Byrne, an early Kennedy supporter, sidestepped questions on whether she would support Sen. Edward M. Kennedy (D-Mass.) should hhe seek the Democratic presidential nomination next year. CAPTION: Picture, Byrne, with Denver Mayor William McNichols, speaks to reporters in Pittsburgh. AP