Speaking to The Anadolu Agency on Friday, South Sudanese army spokesman Philip Aguer said Khartoum had long wanted to declare war on South Sudan and that his government was taking the Sudanese remarks seriously.
Aguer denied claims that rebel groups fighting the Khartoum government were being sheltered by South Sudan, asserting that such claims aimed to justify a declaration of war on his country.
Sudanese authorities have accused Juba of backing and sheltering rebels opposed to the Khartoum government.
Earlier this week, Sudanese intelligence chief Mohamed Atta hinted that Sudanese forces would pursue rebels that staged "hostile" acts against Khartoum from South Sudanese territory.
Juba, for its part, denies Khartoum's accusations that it provides support to anti-Sudan rebels.
South Sudan seceded from Sudan in 2011 in line with a 2005 peace treaty that ended Africa's longest civil war.
Since 2011, a number of rebel groups have waged an active insurgency against the Khartoum government, particularly in the southern and western parts of Sudan.