Col. Philip Aguer said three of the attacks were on Wednesday and one was on Thursday. He did not give a death toll.
South Sudan broke away from Sudan last year after a self-determination vote for independence. That vote was guaranteed in a mediated end to decades of civil war between the two sides.
But the sides never fully agreed where their shared border lay, nor did they reach agreement on how to share oil wealth that is pumped from the border region.
Instead, the two countries have seen a sharp increase in violence in recent weeks, especially around the oil-producing town of Heglig.
Aguer said southern troops repulsed one attack by Sudanese troops near Heglig on Wednesday and two attacks in Northern Bahr el Ghazal state. One was repulsed in Western Equatoria state early Thursday, he said.
South Sudan government spokesman Barnaba Marial Benjamin said South Sudan does not consider itself at war with Sudan, but he said the south is defending territory it believes it owns based on borders outlined in 1956, when British colonial forces left.
"Up to now we have not crossed even an inch into Sudan," Benjamin said. He added: "The Republic of South Sudan considers the Republic of Sudan to be a neighbor and a friendly nation."
Benjamin said that southern forces would withdraw from Heglig if the African Union guarantees a cessation of hostilities, an agreement on border demarcation, and the withdrawal of Sudanese forces from the nearby border region of Abyei, with Ethiopian troops moving in as peacekeepers.
Sudan President Omar al-Bashir on Wednesday threatened to topple the South Sudan government after accusing the south of trying to take down his Khartoum-based government.
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