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.
He said it was time for his country to pursue rebel groups that had "committed aggression against Sudan" from bases located on South Sudanese territory.
Earlier Friday, Atta – along with Sudanese Defense Minister Abdel-Rehim Mohamed Hussein – visited South Darfur State on the border with South Sudan to inspect preparations currently underway for countering rebel groups, according to the television channel.
The channel quoted Hussein as saying that ongoing military preparations had "sent a message" to the rebels and their supporters both inside and outside Sudan.
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.