South Sudan seceded from Sudan in July under a 2005 peace deal that ended decades of civil war. The new nation took with it about three quarters of the country's oil output but must still pipe crude through Sudan to the Red Sea terminal at Port Sudan to export it.
The two sides have failed to agree how much the South should pay to do this, and Khartoum has started taking southern oil to make up for what it says are unpaid fees.
"Yesterday (Monday) we have been informed that the government of Sudan has again stolen 2.4 million barrels of our best quality crude oil," South Sudan's chief negotiator, Pagan Amum, said.
South Sudan last month shut down its roughly 350,000 barrels per day of oil production. Amum did not specify where and how Sudan was able to seize the additional 2.4 million barrels, but Sudanese officials previously said there was oil left in the pipeline even after the shutdown and that Khartoum would continue to confiscate what it considered its fair share until the two sides reached a deal.
They met on Tuesday in the Ethiopian capital of Addis Ababa, but the talks finished again without resolving the dispute.
Sudan's foreign ministry spokesman could not immediately be reached to comment on the accusation.
Amum said Sudan had released two vessels that had been waiting to load South Sudanese crude at Port Sudan but another six had arrived. Eight in total are now prevented from entering the port, he said.
"Six vessels were ready to come and load oil that they already bought, but they are not allowed to come to Port Sudan," he said. "These companies are not coming because they have been informed that the oil they bought from South Sudan has been stolen by the government of Sudan."
South Sudan claims Khartoum has "illegally loaded" more than 6 million barrels of its oil since late last year.
This included 1.2 million barrels taken in December, four shipments totaling roughly 2.5 million barrels in January and another 2.4 million barrels reported this month, according to figures provided to Reuters by South Sudan's negotiating team in Addis Ababa.
Correspondence between oil firms and government officials, which South Sudan provided to reporters this month, confirmed that four January cargoes were loaded, but the other seizures could not be independently verified.
Industry sources have said Sudan has sold at least one cargo of confiscated oil is offering more. South Sudan's negotiators did not specify how much of the other crude was intended for use in domestic refineries and how much was meant to be exported.
Sudanese officials have said the country is entitled to a share of the oil because South Sudan has refused to pay the related fees since it seceded, fuelling inflation and a foreign currency shortage in the northern country.