Uganda's President Yoweri Museveni has given the northern Lord's Resistance Army (LRA) rebels an ultimatum of 31 January 2008 to conclude a peace deal.
Mr Kony remains in DR Congo because of the ICC warrant
It is the same date that has been set for LRA leader Joseph Kony and his fighters to leave their jungle hideout in the Democratic Republic of Congo.
DR Congo's army has warned it will launch an offensive if they do not go.
An LRA delegation has just returned to South Sudan, the venue of peace talks, after a six-week tour of the north.
The rebel representatives were discussing issues such as reconciliation in the region which has endured the brunt of a 21-year rebellion.
An estimated 1.5m people remain in displacement camps and thousands were killed during the fighting.
Mr Kony and three other top LRA commanders are wanted by the International Criminal Court (ICC) for war crimes.
Correspondents say this issue has been a stumbling block to finding a lasting peace deal at talks in Juba, the capital of South Sudan.
South Sudan has been hosting negotiations between the government and LRA since mid 2006.
According to Uganda's Monitor newspaper, Mr Museveni said at a meeting with the rebel LRA delegation earlier this week that if no progress was made by the end of January, a new military offensive would be launched.