Museveni told hundreds of people in a stadium in the northern town of Gulu minutes after midnight that his forces were poised to use force to fight the Lord's Resistance Army (LRA) and kill its commanders.
"If the rebels do not come out of the bush, we are going to fight and kill them," he said. "They should respect the ceasefire. If they don't, we shall pursue them and kill them."
He did not say, however, whether he will extend the ceasefire period.
"For 47 days since the ceasefire was declared, nothing has been achieved," Museveni told the cheering crowd at Pece stadium in the city 360km north of the capital, Kampala.
"The army is going to maintain pressure, but negotiations will continue. The combination of both the military option and dialogue will bring peace in northern Uganda," the president said.
Museveni on 14 November announced a limited ceasefire to allow the insurgents to gather in specific areas of northern Uganda to discuss the possibility of launching serious peace talks.
But talks between the Ugandan government and separatists this week failed to clinch a ceasefire that would allow peace talks aimed at ending an 18-year insurgency in northern Uganda. The temporary truce expired on 31 December.
Room for negotiations
"The president however said that the door for negotiations will be left open and called on the rebel leaders, [LRA leader] Joseph Kony and [senior commander] Vincent Otti, to surrender or the army will have no alternative but to kill them," Museveni's spokesman Onapito Ekomoloit said.
President Yoweri Museveni says
there is still room for talks
The ceasefire was supposed to expire on Friday, but contacts had been going on between the rebels and mediators - including religious leaders, diplomats and UN officials - and both the LRA and the government were to sign a draft memorandum of understanding on Friday that would lead to a cessation of hostilities.
The rebels failed to sign the document as members of peace groups, government officials, diplomats and UN officials waited for hours in the town of Kitgum, 80km north of Gulu.
Government negotiator Betty Bigombe said on Friday afternoon the signing of a truce was postponed to give the rebels more time to consult each other.
"We are told that there are disagreements among themselves (LRA rebels)," army spokesman Major Shaban Bantariza said on Saturday, without elaborating.
"It is good the international community has witnessed what has happened," President Museveni said. "The bishops and diplomats were here, but it is the rebels who refused to sign the ceasefire memorandum of understanding.
"We are told that there are disagreements among themselves"
Major Shaban Bantariza,
Ugandan army spokesman
Bantariza also said: "We have orders to resume full operations. The ceasefire expired last night and in Uganda it is now full operations against LRA rebels which started at 7am."
LRA rebels have also reportedly attacked an army vehicle 16km from the northern town of Gulu, shortly after dawn and one soldier went missing during the incident after the truce ran out at midnight (0900 GMT), according to military sources.