Salih al-Mutlaq spoke as Iraqi political leaders prepared to resume talks at 7pm (1300 GMT) on Tuesday in a bid to finalise the charter, which parliament must approve by next week's deadline.
A second round of talks was postponed by a severe sandstorm on Monday.
Al-Mutlaq said the Tuesday meeting would concentrate on federalism. He said the Sunni Arab bloc might formally submit a proposal to delay a decision on the contentious issue until the new parliament took office.
"I think they will accept it because there is no alternative. We will not accept federalism in these circumstances," said al-Mutlaq, who like most Sunni Arabs fears that federalism might divide Iraq.
Sunni Arabs are expected to take a bigger role in the elections planned for 15 December.
Talks were postponed due to a
severe sandstorm on Monday
Many of them boycotted the 30 January vote after calls by religious leaders and threats by armed groups.
Sunnis, who make up 20% of Iraq's population, currently hold
only 17 seats of the 275-member parliament.
The Kurds, who have enjoyed self-rule in the north since 1991, have demanded that the new constitution codify federalism to prevent a future government from curbing Kurdish autonomy.
However, al-Mutlaq said if the Kurdish demands were met, "they will have grave consequences."
He did not elaborate, but the strong language underscores the depth of passion which the issue of federalism evokes on both sides.
Al-Mutlaq also called for more political groups to join the constitutional discussions because the future of Iraq is at stake.
It was unclear whether Kurdish leader Massoud Barzani, head of the Kurdistan Democratic Party and an outspoken champion of federalism, will attend Tuesday's meeting.
Barzani has been delayed in the north due to bad weather in Baghdad, unable to reach the capital. Sandstorms eased in the Baghdad area on Tuesday, but visibility was still limited.