Ruhakana Rugunda, the internal affairs minister and head of the Ugandan government's peace team, told Reuters: "We don't accept changing the venue to Nairobi. The seat of the talks is Juba. Juba remains an appropriate venue."
Joaquim Chissano, the UN envoy for the Ugandan conflict and the former president of Mozambique, was expected to attend the talks on Monday.
The LRA's statement came three days after Omar Hassan al-Bashir, the Sudanese president, vowed to "get rid of the LRA from Sudan".
Ojul said in a statement: "In the circumstances and due to security considerations, the LRA delegation for the peace talks are not going back to Juba but would prefer that the talks resume in a neutral venue, preferably in Kenya."
Ojul said he met Chissano on Thursday to explain why the LRA delegation would not be returning to Juba and said South Africa was another desired venue.
He said: "We wonder why the president of Sudan should consider a military option ... when our forces [in south Sudan] are there by agreement of the cessation of hostilities."
Sudanese officials mediating in the peace talks were unavailable for comment.
It was the latest upset in stop-start talks brokered by the regional government of South Sudan to end a two-decade war that has killed tens of thousands and uprooted nearly two million people.
The two sides last month extended a landmark truce until the end of February while talks continue, but little progress has been made towards a final agreement, with both sides accusing each other of violating the ceasefire.
Riek Machar, the chief mediator at the peace talks and also South Sudan's vice president, said he expected the talks to resume on Monday in Juba as planned.
He told Reuters: "Bashir has said such things before.
"If they stay in Nairobi, who will mediate?"
A Kenyan minister who declined to be named said the government could not yet comment on whether it would be willing to host peace talks.
Before moving to the jungles of the Democratic Republic of Congo, the LRA had bases in southern Sudan from which they launched attacks across the border into Uganda.
Chissano arrived in Uganda on Friday morning for talks with government officials and was due to visit the country's war-ravaged north over the weekend.
Analysts say Bashir's comments were aimed at distancing Khartoum from the LRA, whom it sponsored for years in retaliation for Uganda's support for south Sudanese rebels.