Bashir is wanted by the court in The Hague for crimes against humanity, murder, extermination, torture and rape, among other crimes, in the Darfur region in the 2000s.
He was removed by the military on 11 April after sustained protests by large crowds of people in the capital Khartoum.
He is thought to be in prison after being moved from a presidential residence where he was under armed guard.
Okello Oryem, Uganda’s foreign minister, said: “Uganda would not be apologetic at all for considering an application by Bashir.”
Officials confirmed Bashir had been moved from a “safe place” to Kopar Prison on Wednesday morning, fulfilling one of the protesters’ demands.
His fall followed months of street protests against his 30-year rule, which opponents say was riddled with mismanagement and brutality.
The protests have continued as their leaders say the ruling Transitional Military Council (TMC) must hand power to a civilian-led authority ahead of elections.
An estimated 300,000 people died during a military campaign to end an insurgency in Sudan’s western Darfur region over a decade ago.
The ICC says in its indictment: “A core component of that campaign was the unlawful attack on part of the civilian population of Darfur.
“During the campaign, (Government of Sudan) forces allegedly committed crimes against humanity, war crimes, and crimes of genocide… carried out numerous unlawful attacks, followed by systematic acts of pillage, on towns and villages… subjected thousands of civilians… to acts of murder, as well as to acts of extermination… subjected thousands of civilian women… to acts of rape… and encouraged members of other tribes… to resettle in the villages and lands previously… inhabited.
“Omar Al Bashir… played an essential role in coordinating the design and implementation of the… plan; and used such control to secure the implementation of the… counter-insurgency campaign.”
The Darfur conflict resulted in a refugee crisis that affected several countries in the surrounding region as more than a million people fled their homes.
Mr Oryem said Bashir had yet to contact Kampala to seek asylum, but added he thought that there was no harm in considering such a claim if one was to come in.
The ICC is yet to comment.
ICC member states, including Uganda, are required to hand over anyone who enters their territory who is under indictment.
Russian and North Korean leaders meet for first summit
The two shook hands as they met in the far eastern city of Vladivostok on Thursday, with the Russian president saying he is “confident” the meeting will develop ties between their countries.
Mr Putin said he welcomed Mr Kim’s efforts to normalise relations with the US, despite talks between those two countries having stalled.
He also said Russia would like to help resolve the nuclear stand-off.
There have been no known high-level talks since and North Korea appears to have lost patience.
“We welcome your efforts to develop an inter-Korean dialogue and normalise North Korea’s relations with the United States,” Mr Putin told Mr Kim.
Last week they tested a new weapon and said they no longer want to deal with US secretary of state Mike Pompeo, calling for him to be replaced in discussions by someone “more mature”.
When he arrived in Russia, Mr Kim said he wanted to talk with Mr Putin about ties between their countries and the “settlement of the situation in the Korean Peninsula”.
He told Russia’s state-owned Rossiya-24: “I have heard a lot about your country and have long dreamt of visiting it.
“It’s been seven years since I took the helm, and I’ve only just managed to visit.”
Mr Putin’s foreign affairs adviser, Yuri Ushakov, said the Russian president would seek to “consolidate the positive trends” from Mr Trump’s meetings with Mr Kim.
Mr Ushakov said Russia’s trade with North Korea fell by more than 56% last year because of sanctions against Pyongyang.
Russia would like more access to North Korea’s mineral resources and North Korea wants Russian investment to help develop its infrastructure.
But there will also be some time for Mr Kim to meet “ordinary people” and a chance to try traditional Russian food such as pelmeni meat dumplings and caviar during his visit, according to reports.
The visit has seen an increase in security in Vladivostok, a city of more than 600,000, and local media say some platforms at the main train station will be closed for several days and buses diverted.
Vehicles have also been banned from the city centre and maritime traffic will not be allowed near the summit venue Russky Island.
21 killed as heavy storm sweeps South Africa
The deaths were reported in KwaZulu-Natal (KZN) Province where heavy storms battered various parts of the province on Monday night, the provincial department of cooperative governance and traditional affairs said in a statement, NAN reports.
“Last night, the weather conditions worsened significantly across KZN and the heavy rain culminated in various parts of the province, claiming at least 21 lives and 32 patients in and around Durban,’’ the statement said.
Rescue teams have been responding to the incessant rain that has wreaked untold damage on the communities, said the statement.
It said efforts are being made to minimise the impact of the storm on the residents and businesses.
The Eastern Cape and Northern Cape provinces also experienced severe weather conditions.
In Port St Johns in the Eastern Cape, serious flooding prompted the South African Air Force to dispatch helicopters to assist with rescue operations.
The flooding forced the evacuation of hundreds of people to community halls and churches since Monday.
“Minister of Defence and Military Veterans Ms NN Mapisa-Nqakula said she has instructed the South African National Defence (SANDF) to help rescue and evacuate those affected by this natural disaster,’’ the SANDF said in a statement.
Kim Jong Un arrives in Russia ahead of summit with Putin | World News
The two leaders will meet in the far eastern Russian city of Vladivostok amid tensions surrounding the North Korean leader’s nuclear programme.
Mr Kim, dressed in a black coat and a fedora, met with officials who welcomed him with traditional Russian bread and salt at the station.
The leader had a sit down with local officials as well as a Russian deputy foreign minister before continuing on his journey to Vladivostok.
Mr Kim was quoted on the local administration’s website as saying: “I have heard a lot about your country and have long dreamt of visiting it. It’s been seven years since I took the helm, and I’ve only just managed to visit.”
He reportedly said he echoes his father’s “great love for Russia” and that he intends to strengthen the relationship between the two countries.
Mr Kim is the first North Korean leader to travel to Russia since his late father, Kim Jong Il, visited in 2011.
Moscow is interested in gaining broader access to North Korea’s mineral resources, including rare metals.
Pyongyang needs Russia’s electricity supplies and wants to attract Russian investment to modernise its Soviet-built industrial factories, railways and other infrastructure.
Kremlin adviser Yuri Ushakov said Russia’s bilateral trade with North Korea fell by more than 56% last year because of sanctions against Pyongyang.
He added Moscow believes it is important that North Korea and the United States are interested in maintaining their contact.
North Korea has said it no longer wants to deal with US secretary of state Mike Pompeo, and has called for him to be replaced in denuclearisation discussions by someone “more mature”.
Mr Kim has had two summits with US President Donald Trump, but the latest one in Vietnam collapsed in February.
North Korea wanted more sanctions relief than the United States was willing to give for the amount of nuclear disarmament.
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