Lokudu said the killings in Western Bahr al-Ghazal state were motivated by anger that many people in the area had voted for the NCP.
South Sudanese denial
Parties and independents opposing the SPLM, which leads the semi-autonomous government in the south, have previously complained of arrests and harassment, but the SPLM denied that the separate south Sudan army was involved in the incident.
"This was a passionate crime to do with a wife - a feud that led to a shooting between the husband and lover," Suzanne Jambo, the head of the SPLM's external relations office, said.
"This is not political."
There has been little violence during the five days of voting in the country's first multi-party polls in 24 years, despite tension sbeing increased by boycotts of various parts of the process by opposition parties amid allegations of irregularities.
The SPLM pulled out of parliamentary voting in most northern states and withdrew Yasser Arman as a candidate for the presidency. The Umma party also pulled it candidate out the presidential race.
Those decisions left little competition for Omar Hassan al-Bashir, the current president and leader of the NCP, as he attempts to secure another term.
Ruling party offer
Bashir's supporters, however, seemed to reach out to the opposition parties on Wednesday, saying the NCP would invite opposition groupsto join the government if it won the current elections.
"If we are declared winners in the elections ... we would extend the invitation to all parties, even those who have not participated in the elections, to join the government," Ghazi Salaheddin, a senior leader of the NCP said.
Bashir's rivals gave a mixed reaction to the offer, which did not specify what parts they might play in a new government.
"Let us talk about dialogue first, how to solve Sudan's problems," Fadlalla Burma Nasir, the vice-president of the opposition Umma party, said.
The SPLM's Arman said he was not interested in the offer and levelled further accusations of fraud against the ruling party.
"This is proof that they know the results in advance," he said.
Results of the elections are not expected until April 20.