"South Sudan continues to offer logistical and financial support to rebel movements," Sudanese Foreign Ministry spokesman Yousif al-Kordofani said.
"This runs counter to the spirit demanded in relations between the two states," he added in statements to the press.
He called on the government of South Sudan to immediately refrain from backing Sudanese rebel movement.
He said relations between Sudan and South Sudan ought to be based on clear foundations aiming at protecting their stability.
The Anadolu Agency could not immediately obtain comments from the government of South Sudan on al-Kordofani's remarks.
Juba had, however, several times in the past denied accusations in this regard.
On Friday, Sudanese intelligence chief Mohamed Atta warned South Sudan against supporting or sheltering rebels fighting the Khartoum government.
He said Sudan would crack down on rebel groups – even those found on South Sudanese territory.
"The army and rapid-reaction troops will crack down on the rebels on South Sudanese territory," Atta was quoted as saying by the pro-Khartoum Ashorooq television channel.
"Sudan is running out of patience with South Sudan, which shelters militant movements that come to Sudan to destabilize it," Atta reportedly added.
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.