"My understanding is that these remarks contradict the Comprehensive Peace Agreement (CPA), according to which priority must be given to unity," Mandour al-Mahdi, an NCP official, said on Sunday.
The remarks were contained in a statement quoted by the official Suna news agency.
Kiir's comments have added pressure to the already troubled relationship between his Sudan People's Liberation Movement (SPLM) and the north's dominant NCP.
Both sides promised to build up a campaign to make the unity of Sudan attractive to voters when they signed the peace deal, or CPA, in 2005.
The mainly Christian and animist south will vote in the 2011 referendum as part of the CPA, which ended a 22-year war with the mainly Arab Muslim north.
"You want to vote for unity so that you will become a second-class in your own country, that is your choice"
President, South Sudan
Sudanese nationals began on Sunday to register for the general election scheduled for April, the country's first in 24 years.
It will be followed by the referendum.
In his controversial remarks, made in Juba, the South Sudan capital, Kiir said: "You want to vote for unity so that you will become a second-class in your own country, that is your choice.
"If you would want to vote for independence so that you are a free person in your independent state, that will be your own choice."
Tensions have been running high between north and south, still divided by the religious, ethnic and ideological differences over which the civil war was fought.
US envoy's trip
Against this backdrop, Scott Gration, the US special envoy to Sudan, travelled to Juba on Saturday and met Kiir.
The US has facilitated talks between the northern and southern governments on power and resource sharing.
Barack Obama, the US president, launched a new carrot-and-stick policy this month aimed at ending violence in Sudan's Darfur region and the south.
Two million people were killed and four million fled their homes between 1983 and 2005 as the north and south battled over differences of ideology, ethnicity and religion.
North Sudan is mostly Muslim while southerners are largely Christian and followers of traditional beliefs.