(CNN) -- Rep. Charlie Rangel, D-New York, said Friday that he is taking the congressional ethics investigation now threatening to derail his career "one step at a time."
"I'll be glad to see what happens Thursday" when the House ethics subcommittee responsible for conducting formal hearings has its first organizational meeting, he said. "This thing is coming to a head."
Rangel added, however, that "nobody in his right mind (would be) looking forward to something like this."
Rangel recently stepped down as Ways and Means chairman following the announcement of a congressional investigation into several allegations, including failure to pay taxes on a home in the Dominican Republic.
The congressman has also admitted a failure to report several hundred thousand dollars in assets on federal disclosure forms.
In addition, he is under scrutiny for the purported misuse of a rent-controlled apartment for political purposes, as well as for allegedly preserving tax benefits for an oil-drilling company in exchange for donations to a project he supported at the City College of New York.
The House ethics committee previously admonished Rangel for violating rules on receiving gifts. Specifically, the committee found that Rangel violated House gift rules by accepting reimbursement payments for travel to conferences in the Caribbean in 2007 and 2008.
Rangel, who has served 20 consecutive terms in the House, has several challengers in his district's Democratic congressional primary this year. Among those seeking to replace him is the son of the late congressman Adam Clayton Powell Jr., who was ousted by Rangel 40 years ago.
Rangel said Friday he wants "people to know who Charlie Rangel was, is, and is proud to be" before the September 14 primary. People should know "how awkward it has been for me to constantly" tell them to wait until the ethics investigation is over before commenting, he added.
It is tough not to respond to the "mean" things said about me, he declared.
"I won't let you down," he promised his constituents.
Rangel also said he had called MSNBC's Luke Russert to apologize for his treatment of Russert during an exchange on Capitol Hill Thursday. Pressed by Russert on the possibility of losing his office, Rangel accused Russert of "trying to make a name" for himself, and said the young journalist was asking "dumb questions."
"It doesn't really sound like NBC asking these dumb questions," Rangel said. "It just shows what happened to a channel that did have some respect."
The adjudicatory subcommittee that will consider Rangel's case is composed of four Democrats and four Republicans, according to an ethics committee document.
It says Rep. Zoe Lofgren, D-California, is the panel's chairperson.
Other Democratic members are Rep. G.K. Butterfield of North Carolina, Rep. Kathy Castor of Florida and Rep. Peter Welch of Vermont. The four Republicans are Rep. Michael McCaul of Texas, Rep. Mike Conaway of Texas, Rep. Charlie Dent of Pennsylvania and Rep. Gregg Harper of Mississippi.
CNN's Alan Silverleib and Deirdre Walsh contributed to this report