Powell, appearing on "Face the Nation" Sunday, answered criticism from Cheney, who questioned Powell's loyalty to the GOP after voting for President Barack Obama in November.
"I am still a Republican. I'd like to point out that in the course of my 50 years of voting for presidents, I have voted for the person i thought was best qualified at that time to lead the nation.
Last year I thought it was President-now Barack Obama," Powell said.
Powell said the Republican party needs a new look if it wants to stay relevant.
"I think the Republican party has to take a hard look at itself and decide what kind of party are we?" he said.
"I have always felt that the Republican party should be more inclusive than it generally has been over the years.
Powell also addressed criticism from conservative radio host Rush Limbaugh, saying his assertion that Powell only voted for President Obama because "he is black" was "unfortunate."
He admitted the influence Limbaugh has over the GOP is significant, noting the apologies he has solicited from major party figures including RNC Chairman Michael Steele.
"If he is out there, he should be subject to criticism," Powell argued. He said that while Limbaugh is perfectly allowed to have an opinion, he does not have "veto" rights over the opinions of others.
On Face the Nation earlier this month, former Vice President Cheney said that Rush Limbaugh better represents the Republican party than Powell. Clearly, the former Bush Secretary of State has other ideas.
More from Face The Nation (5.24.09):
To watch Colin Powell address the future of the GOP, click below: