Kenyan President Uhuru Kenyatta began a two-day visit to Sudan on Saturday, just days after Khartoum issued a call to all African countries to withdraw from the International Criminal Court.
Sudan has urged African members to quit the Hague-based ICC which it said was a "new colonial tool" against African leaders, after South Africa announced its decision to withdraw last week.
Kenyatta, who was himself investigated by the ICC over deadly 2007-2008 post-election violence, was welcomed at Khartoum airport by his counterpart Omar al-Bashir, who is also wanted by the ICC on war crimes charges related to the conflict in Darfur.
The ICC was dealt a blow last week when South Africa announced its intention to withdraw.
Burundi had already declared its intention to withdraw, and earlier this week Gambia became the latest African nation to follow their lead.
The ICC, created in 2002, is often accused of bias against Africa and has struggled with a lack of cooperation, including from the United States, which has signed the court's treaty but never ratified it.
Of the 10 ICC investigations since 2002, nine have been into African countries and one into Georgia -- and most ICC cases have been referred to the court by African governments themselves.
Pretoria's decision followed a dispute last year when South Africa faced international condemnation for not arresting Bashir when he visited for an African Union summit.
Kenyatta and Bashir are expected to discuss Kenya's possible withdrawal from the ICC, Sudanese officials said.
"President Kenyatta's visit comes at an important time," Sudan's Minister of State for Foreign Affairs Kamal Ismail told reporters at Khartoum airport.
Asked specifically about Kenya's possible withdrawal from the ICC, Kamal replied: "This is an issue for Kenya. When it decides to withdraw is something that Kenya will decide."
The ICC faced a severe setback in late 2014 when prosecutors dropped a crimes against humanity case against Kenyatta for his alleged involvement in post-election violence in the east African country.
Bashir is wanted by the ICC for war crimes and genocide related to the conflict in Darfur, which has left at least 300,000 people dead, according to the United Nations.