Zebari urges Maliki to apologise
In an exclusive BBC interview, Mr Zebari said that unless Mr Maliki withdrew his remarks, Kurds would find it very difficult to work with him.
Kurdish ministers have suspended participation in government in protest.
The row between the autonomous region and the Baghdad authorities threatens to further destabilise the country.
Kurds have seized areas left by Iraq's army as jihadist militants advanced.
Mr Zebari said that relations between the Baghdad government and the Kurds had "never been so poisonous".
He said the disagreements centred on the sharing of oil revenue and the Iraqi annual budget.
Disputes between the ethnic Kurds of northern Iraq and the majority Arabs go back for decades.
The BBC's Mark Doyle in Baghdad says the crisis has rarely been so serious, or dangerous, as now.
A Kurdish announcement that it was actively preparing for a referendum on independence within months came at the height of a separate and massive rebellion by violent Islamists.
Baghdad is furious with the Kurds over the referendum bid, our correspondent says.
