The Sudan People's Liberation Army-North "ambushed and captured a vehicle loaded fully with ballot boxes" on Saturday on the road linking the state capital Kadugli with the town of Dilling, spokesman Arnu Lodi said on Sunday.
The SPLA-N will press its "military campaign plan" to stop elections in South Kordofan, Lodi said in the statement, warning civilians to avoid military sites "because they are legitimate targets".
But army spokesman Colonel Al-Sawarmy Khaled Saad told AFP he had no information on the ambush.
Last month the SPLA-N announced its campaign to disrupt presidential and legislative elections slated for April 13.
Sudan's mainstream opposition is boycotting the elections, which are widely expected to extend the rule of President Omar al-Bashir, 71.
Bashir's government has been battling the SPLA-N in South Kordofan and Blue Nile states since 2011.
The SPLA-N has said the armed campaign intends to integrate "the various means of struggle, armed uprising and civil disobedience, to work together to stop the elections".
Their political wing signed the Sudan Call agreement aimed at uniting the opposition in Addis Ababa in December, along with political parties, civil society organizations and other armed groups.
The group is boycotting the elections but several signatories have denied the SPLA-N's campaign to disrupt the elections is Sudan Call's armed wing.
Representatives for Sudan Call had been due to meet members of Sudan's ruling National Congress Party (NCP) in Addis Ababa at the end of March to discuss a national dialogue promised by Bashir last January.
The dialogue was supposed to address Sudan's problems and end the insurgencies in Blue Nile, South Kordofan and the western region of Darfur.
The NCP did not attend and said the pre-dialogue meeting would take place after voting.
UN Secretary-General Ban Ki-moon voiced his "disappointment" at the meeting's failure.
Sudan Call sharply criticized the NCP in a statement on Sunday, urging Sudanese to "escalate resistance to the fake elections," but did not say whether they would attend talks after the vote.
Violence has risen over the past month in South Kordofan and Blue Nile, and the government said last week fighting since the beginning of March alone had displaced at least 20,000.
Despite this, Defense Minister Abdel Rahim Mohammed Hussein said on Friday the army "will not allow the rebels to impede elections".
And Bashir has pledged to bring peace to conflict-stricken states, either by force or through talks.
Bashir, a career soldier, came to power in a 1989 coup and has been indicted by the International Criminal Court over alleged war crimes in the western region of Darfur, where he is battling a separate insurgency.