“Good morning, everyone,” Mr. Bloomberg said, looking around at the packed seats, rows of manned video cameras and reporters standing in the wings for a press conference about energy conservation. “Big crowd.”

The Mayor’s quiet move last week to drop his Republican affiliation has fueled all sorts of theories that he might mount an independent Presidential run. It has also, to his apparent delight, forced the press to hang on his every nasal, monotone word. For the moment, he has eclipsed his Republican predecessor, Rudy Giuliani, and Democratic front-runner Senator Hillary Clinton in media interest, coyly denying any national ambitions while discussing national issues far outside his official purview.

One week in, the press already seems a little tired of it.

“Since you told us numerous times you are not running for President, there has been all this speculation,” said New York Post City Hall bureau chief David Seifman at the press conference on Monday. “Can you advise the press to stop writing about all this?”

“I think the press should start writing about the things that are changing in this city,” Mr. Bloomberg responded, before segueing into a catalog of city accomplishments including lower crime, higher test scores and a stronger economy since Sept.11. “Those are the things that I am working on and will continue to work on. I think it’s a great story and it’s a great story for the country.”

It was on the afternoon of June 20 that Mr. Bloomberg, dressed in a dark business suit, blue shirt and crimson tie, made his first public appearance as an independent. It was at a hastily organized press conference to mark the occasion of the 50 millionth caller to the city’s 311 line.

Under high ceilings at the Maiden Lane offices, Mr. Bloomberg faced more than a dozen television cameras, a parapet of kneeling photographers and squinting reporters studying him for telltale signs of Presidential ambition.

City information-technology commissioner Paul Cosgrave sarcastically commented that everyone had obviously showed up for the 311 milestone.

“That’s why they’re here,” said the Mayor.

Fidgeting with a pen and propping his elbows up on a cubicle wall off to the side, Mr. Bloomberg’s closest political aide, Kevin Sheekey, watched closely. Early last year, Mr. Sheekey had planted the Bloomberg for President story line with some of the very same reporters in the room. Back then it seemed like a joke. Now, characteristically tie-less and unusually nervous, he watched the fruits of his labor ripen.

Mr. Bloomberg again asserted he had no interest in running and that he was more than happy in his present job.

“But I’m confident that this country will have options,” Mr. Bloomberg said when asked what he would do if the country proved unsatisfied with the nominees the two major parties offered. “I do think the more people who run for office the better, and then as we narrow it down, people will I think pick and choose and the choices will look good and hopefully this country is smart enough to pick somebody to lead this country forward.”

Egged on by reporters, he then touched on foreign policy toward Iran, hinted at a humanitarian interventionist streak to prevent genocide, aired his opposition to restrictive immigration laws and bemoaned America’s slipping in business and education.

“I feel very strongly I should be out there talking about those issues that influence New York City and that are dealt with at a national level.”

Some reporters complained to one another that, with Bloomberg inching toward the race, their publications were unequipped to cover three hometown Presidential candidates, and that weekends would now become but an undifferentiated extension of the working week.

That night, a previously taped interview with The NewsHour with Jim Lehrer featured Mr. Bloomberg declaring, “The only reason to run for President is to win.” At about the same time it aired, the Mayor walked up the stairs of the Sheraton in midtown Manhattan surrounded by his security detail and Mr. Sheekey. At the top of the stairs, in front of the second-floor ballroom, he stopped for a quick chat with Stuart Appelbaum, a Jewish labor activist hosting the event. Mr. Appelbaum was effusive about the Mayor’s new independent affiliation and the prospects that it opened.

“I’m in awe,” said Mr. Appelbaum.

“We’ll see what happens,” said Bloomberg, nodding his tilted head, shrugging his shoulders. Again he seemed to want to smile.

One floor above, Mr. Giuliani held a fund-raiser for supporters, but reporters opted to listen to Mr. Bloomberg’s speech about labor rather than stake out the Republican Presidential candidate.

The next day, the Mayor’s public schedule listed him as giving remarks at the graduation ceremony at Rockefeller University on the Far East Side at 2 p.m. Almost an hour later, there was still no sign of the Mayor. There had been a miscommunication, his aides said, and he would be speaking after 4. The reporters covering the event—which promised to be entirely devoid of news—waited in the heat and perspired. Mr. Bloomberg eventually appeared, dressed in cap and gown, proceeding into the auditorium with professors and graduates.

While the university professors spoke about science, the Mayor’s press officers took a breather. One aide sat with his legs crossed on the empty stage in the middle of a lawn where the brass band had welcomed the arriving graduates. He read from that day’s press digest, a binder of stories about his boss, including a Daily News article about a conflict between Mr. Bloomberg and Mr. Giuliani.

When the Mayor’s time to speak finally came, he again touched on a national theme.

“Now, I wish some of our nation’s lawmakers could be here today—because this graduating class makes an eloquent argument for why America so urgently needs to revise its immigration policies,” said Mr. Bloomberg. “Our current, wildly unrealistic and unworkable visa restrictions severely handicap international students studying here.”

Mr. Bloomberg has clearly warmed to the Presidential speculation, although, perhaps not surprisingly, he has had some more strongly negative reactions to suggestions that he might be interested in making a bid for any other higher office.

At a press conference about energy conservation on June 25, the Mayor thought he heard a reporter addressing him as Governor—another office for which the Bloomberg name has been floated.

The Mayor quickly pointed out that he was, in fact, the Mayor. And he hastened to add the following: “I have no interest, for the record.”

For once, no one doubted him.