Geithner said in a nationally broadcast interview that President Barack Obama strongly believes those reductions should be retained for the "95 percent" of taxpayers with individual incomes under $200,000 a year and families below $250,000.
And he disagreed with accusations the administration has been hostile to Wall Street and the business community.
Asked about former Federal Reserve Board chairman Alan Greenspan's statement that he hadn't seen such animosity between Washington and Wall Street in decades, Geithner said Obama had a deep obligation "to fix what was broken. There was nobody here or across the country that would argue that our system worked."
"The business community always wants their taxes lowered," Geithner said, calling that understandable.
On another matter, the secretary said he wouldn't be surprised if the 9.5 percent national unemployment rate ticks up again Friday when the Labor Department releases figures for July.
"It's possible you're going to have a couple months where it goes up," he said, "as people start to come back into the labor force. ... That can cause the measured unemployment rate to go up."
Geithner acknowledged the economy is "not coming back as quickly as we'd like."
He said he didn't know if Congress would act on the issue of the tax cut extension before the midterm elections this November, but that "it is the responsibility" of lawmakers to ensure that the issue doesn't fall victim to Capitol Hill gridlock.
Asked on ABC's "Good Morning America" how long he planned to stay in Obama's Cabinet, Geithner replied: "I will stay as long as he asks me to stay."