"We have never refused to acknowledge the liability," Reserve Bank governor Gideon Gono told the Herald newspaper, saying the money would be cleared in seven days.
The Global Fund calculates that the inflation-battered central bank has not released 7.3 million dollars (5.7 million euros) held in its coffers to local commercial banks so that Zimbabwean health programmes can use the money.
"We do welcome this but the money does have to be returned before this is closed. We're still waiting for that to happen," the fund's spokesman Andrew Hurst said in response to the government's promise.
"We want that money to go back to the banks so they can get on with the work of disbursing it to the beneficiaries," he told AFP.
"We're confident that this can be settled."
The unspent funds are part of 12.3 million dollars received by the country's central bank last year, which was meant to help Zimbabwe's people who face a growing humanitarian crisis.
Gono dismissed allegations that the central bank had used the funds to buy tractors and TV sets, the Herald reported.
The former model economy has collapsed over the past decade, with chronic shortages of basic foodstuffs, fuel and foreign exchange.
When Gono was appointed in November 2003, inflation was 619.50 percent but in July the rate hit 213 million percent.
Zimbabwe issued three new denominations of banknotes on Wednesday, including a one-million-dollar note - about two US dollars on the black market - as the impoverished country struggles to cope with runaway inflation.
The Geneva-based Global Fund is a partnership between governments, non-government groups and the private sector set up to secure funding to fight AIDS, tuberculosis and malaria.