The consumer watchdog was established as part of Wall Street reform to make sure Americans have the information they need to make financial decisions such as paying for college or buying a home, Obama said in his weekly radio and Internet address.
The agency will go after "anyone who tries to take advantage of you, or rip you off," the president said.
"Starting this month, that includes the folks who come up with your credit score. ... The companies that put your credit score together can make mistakes. They may think you had a loan or a credit card that was never yours. They may think you were late making payments when you were on time. And when they mess up, you're the one who suffers," Obama said.
"Until this week, if you had a complaint, you took it to the company. Sometimes they listened. Sometimes they didn't. But that was pretty much it. They were your only real hope.
"Not anymore. If you have a complaint about your credit score that hasn't been properly addressed, you can go to consumerfinance.gov/complaint and let the consumer watchdog know."
Obama said the government will give consumers a tracking number "so you can check back and see exactly what's being done on your behalf" and can help with more than just credit scores.
"If you're opening a bank account, trying to get a student loan, or applying for a credit card and something doesn't seem right, you can let them know and they'll check it out.
"If you're looking to buy a home, and you want to know if you're getting a fair deal on your mortgage, you can give them a call and they'll get you an answer.
"Their only mission is to fight for you. And when needed, they'll take action," he said.
"That's what Wall Street reform is all about -- looking out for working families and making sure that everyone is playing by the same rules."
Obama warned that Republicans in Congress "backed by an army of financial industry lobbyists" are trying to dismantle the new rules, adding, "I refuse to let that happen."
"I believe that the free market is one of the greatest forces for progress in human history, and that the true engine of job creation in this country is the private sector, not the government.
"But I also believe that the free market has never been about taking whatever you want, however you can get it. Alongside our innovative spirit, America only prospers when we meet certain obligations to one another, and when we all play by the same set of rules," Obama said.