WASHINGTON (AP) – Rudy Giuliani, the former New York City mayor whose popularity soared after his response to the Sept. 11, 2001 terrorist attacks, moved closer to a full-fledged campaign for the Republican presidential nomination on Monday.

In a sign that he’s serious about running for the White House, the two-term mayor was filing a so-called “statement of candidacy” with the Federal Election Commission. In the process, he was eliminating the phrase “testing the waters” from earlier paperwork establishing his exploratory committee, said an official close to Mr. Giuliani’s campaign.

The official spoke on the condition of anonymity to avoid pre-empting any disclosure by Mr. Giuliani.

Unlike chief GOP rivals Senator McCain and Mitt Romney, Mr. Giuliani has been somewhat ambiguous about whether or not he would ultimately pursue the Republican nomination.

He took the initial step in November of creating a committee to explore a candidacy but added the caveat that he was simply “testing the waters” – a provision that allows truly uncertain candidates to move forward without any commitment to seek a top spot on the ticket or the need to identify donors. At the time, Mr. Giuliani also did not file an official statement declaring that he was a presidential candidate.

The steps Monday put Mr. Giuliani on the same level, legally, as Mr. McCain and Mr. Romney, the other two top-tier GOP candidates who have formed regular exploratory committees and filed statements of candidacy.

Mr. Giuliani’s cautious and noncommittal attitude has caused some critics to publicly question whether he would abandon his bid even before formally entering the race, as he did in 2000 when he was considering a Senate campaign against Democrat Hillary Rodham Clinton.

Fighting back in recent weeks, Mr. Giuliani has started to sound and act like a strong contender, traveling to early primary states of New Hampshire and South Carolina, and arguing that his vision for the future and performance in the past would make him a formidable GOP nominee.

Still, he has stopped short of committing to a run, insisting that he has to decide whether he can make a “unique contribution” to help strengthen the country – his barometer for whether to run.

“There’s a real good chance,” Mr. Giuliani said Saturday, another coy response to what has been a constant question on the campaign trail.

The shift in campaign organization, however slight, is an indication that Mr. Giuliani likes the response he’s received as he gauges support while traveling the country.

Behind the scenes, Mr. Giuliani has been busy supplementing his cadre of New York loyalists with Washington-savvy political operatives, establishing a fundraising network, and setting up a campaign headquarters – signs of a campaign moving forward.

Despite being immensely popular in national polls, Mr. Giuliani faces hurdles to securing the Republican nomination state by state. His moderate stances on issues such as gun control, abortion and gay rights do not sit well with hard-core social conservatives who are a crucial voting group in the nominating contests, and his two divorces may not either.

But conservatives also aren’t entirely sold on Mr. McCain, an Arizona senator, and Mr. Romney, a former Massachusetts governor, and that could even the playing field for Mr. Giuliani. He hopes primary and caucus voters look past his liabilities and consider his record of leadership in difficult times.