"It's a codeword for an agreement that President Bashir delegates another senior cabinet-ranked person. That was agreed," he said.
The Sudanese envoy in Kampala had earlier indicated that al-Bashir was considering making the trip, which would have been his first to a country party to the ICC since the warrant was issued in March.
Isaac Musumba, Uganda's East Africa and regional affairs minister, told parliament on Wednesday that the arrest warrant could make any visit by al-Bashir problematic for Uganda, which is bound to arrest the Sudanese president under the Rome statutes that set up the ICC.
"We wish to avoid a possible diplomatic incident that may arise as a result of a visit by President Bashir"
Uganda's East Africa and regional affairs minister
"We wish to avoid a possible diplomatic incident that may arise as a result of a visit by President Bashir," he said.
"The government is therefore diplomatically engaging the government of the Sudan with a view to ensuring that, while the invitation to President Bashir still stands, a possible diplomatic incident is avoided."
Luis Moreno-Ocampo, the chief prosecutor at the ICC, had reminded Kampala of its obligations to detain al-Bashir during a visit earlier in the week.
Thirty African nations have signed up to the Rome statutes but the African Union, which includes Uganda, earlier this month decided that it would not co-operate with the arrest warrant.
Dismas Nkunda, the chairman of the Darfur Consortium, a coalition of more than 50 Africa-based and Africa-focused NGOs working to end the crisis in Darfur, said that the arraest warrant had created a "dilemma" for African nations.
"They have two things to deal with - one is the political decision to protect Bashir and the other is the legal issue that binds the African countries," he told Al Jazeera from Arusha in Tanzania.
"It comes down to how we should deal with people who have committed crimes on the continent."
Yoweri Museveni, Uganda's president, was the first head of state to invite the ICC to investigate crimes committed on its soil, leading to the eventual indictments of five members of the Lord's Resistance Army rebel group.
The United Nations estimates that 300,000 people have been killed since the conflict broke out in Darfur in 2003. Khartoum says only 10,000 people have died.