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 US presidential nomination on Monday. In a sign that he is serious about running for the White House, the two-term mayor filed a so-called "statement of candidacy" with the Federal Election Commission, indicating that he would seek the presidency as a Republican should he decide to go forward. Unlike chief Republican rivals Sen. John McCain and former Gov. Mitt Romney, Giuliani has been somewhat ambiguous about whether or not he will ultimately pursue the Republican nomination, even though he has taken the initial steps. In recent weeks, Giuliani's cautious and noncommittal attitude has caused some critics to 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 lately, Giuliani has started to sound and act like a strong contender, traveling to the early primary election 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 Republican nominee. Behind the scenes, 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. Publicly, however, 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," Giuliani said Saturday in South Carolina, another coy answer to what has been a constant question on the campaign trail. However slight, the shift in campaign organization is an indication that Giuliani likes the response he has received as he gauges support while traveling the United States. In November, Giuliani took the initial step 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, Giuliani also did not file an official statement declaring that he was a presidential candidate. The steps Monday, including eliminating the phrase "testing the waters," put Giuliani on the same level legally as McCain and Romney, the other top-tier Republican candidates who have formed regular exploratory committees and filed statements of candidacy. Despite being immensely popular in national polls, 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. His two divorces could be obstacles as well. But conservatives also are not entirely sold on McCain, an Arizona senator, and Romney, the former Massachusetts governor, and that could even the playing field for Giuliani. He hopes primary and caucus voters look past his liabilities and consider his record of leadership in difficult times.