The National Congress Party (NCP) has accused the Sudan People's Liberation Movement (SPLM) of acting in bad faith for threatening to withdraw its members from parliament.
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But the NCP dismisses the charge as unwarranted.
The SPLM's proposals include a security and intelligence service, a referendum that could lead to southern Sudan's self determination, and a budget measure.
Analysts say the SPLM's latest threat could worsen tensions with its northern partners.
Ezekiel Lol Gatkuoth, head of southern Sudan's mission to the United States said that his party is "only" promoting the wishes of the Sudanese people.
"It is not true that we are obstructing the implementation of the CPA. This is the only thing that we want to see happening. The CPA, we wanted it to be implemented in this opening of the parliament," Gatkuoth said.
<!-- IMAGE -->He said SPLM members want parliament to discuss and endorse its proposals.
"We just wanted the freedom law to be passed, the laws that are actually meant for democratic transformation, and then the budget. These are the three items that we wanted to be discussed in the parliament," he said.
Gatkuoth said his movement is fighting for the ordinary Sudanese.
"This is not our wish. It is the wishes of the people of Sudan. They want this agreement to be implemented (and) we are actually saying that the National Congress Party should not deviate from what we have agreed upon," Gatkuoth said.
He said Sudanese want to feel free in their own country.
"They want a democratic country and a country that is transformed, whereby it respects all the religions, respects all the aspirations of everybody in Sudan," he said.
Gatkuoth said its northern partners often make decisions without the SPLM's input, a charge the NCP denies.
"Decisions are being made using a mechanical majority without the consensus of the two parties - (like they) expelled the Canadian diplomat. They are doing things unilaterally without consulting with us," Gatkuoth said.
He denied the SPLM is threatening its northern partners.
"We are not threatening anybody. The only thing that is binding the National Congress Party and the SPLM together is the CPA. Short of that, we are not partners," he said.
<!-- IMAGE -->Gatkuoth said the NCP is determined to move the country towards an Islamic state despite the SPLM's protests.
"These two parties have different ideologies. The National Congress Party … they want to Islamize the whole world. That is their thinking, and that is their ideology. For us, we are saying that everybody is equal in this country of ours called Sudan," Gatkuoth said.
The 2005 Comprehensive Peace Agreement effectively ended more than two decades of civil war between the Sudanese north and the south.
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