He is accused of orchestrating murders, rapes, and torture during the conflict between between rebels groups and government forces backed by local militias.
"There is a general concern in Africa that the issuance of a warrant of arrest for... al-Bashir, a duly elected president, is a violation of the principles of sovereignty guaranteed under the United Nations and under the African Union charter," Mutharika said.
"Maybe there are other ways of addressing this problem. Let us together explore this possibility."
Delegates from 53 countries across Africa are meeting in the Ugandan capital for an African Union (AU) summit expected to focus on security in Somalia, but Bashir himself is not expected to be among them.
An initial draft of a resolution to be passed at the African Union (AU) meeting in Ugandan capital Kampala, seen by the Reuters news agency on Saturday, contained two contentious clauses about the arrest warrants.
But both paragraphs were removed after arguments that went on until the early hours of Sunday, AU and Western diplomats said.
The first clause advised African countries not to arrest Bashir if he visited their nations, even if they were signatories to the Rome Statute which established the ICC and obliges them to carry out its arrest warrants.
"[The AU] reiterates its decision that AU member states shall not co-operate with the ICC in the arrest and surrender of President Bashir," the paragraph said.
Thirty African nations are members of the ICC.
The second deleted clause attacked Luis Moreno-Ocampo, the ICC prosectuor leading thecase against Bashir.
Jean Ping, the AU Commission chairman, has said the decision to prosecute Bashir has undermined peace efforts in Sudan.
The summit is taking place two weeks after Somalia's al-Shabab fighters bombed Kampala in an attempt to force Uganda to withdraw its troops from their country and opened on Sunday with a solemn two-minute silence for the victims of the attack.
African leaders have condemned al-Shabab and pledged to beef up an African force fighting the group.
Ping called the al-Shabab attacks, which left at least 76 people dead, "despicable" and said the continental body was ready to step up its response.
"The commission is already planning the next phases in the deployment of Amisom in terms of the enlarged mandate, increased troop strength and appropriate equipment," he said.
Al Jazeera's Andrew Simmons, reporting from Kampala, said that a more aggressive approach towards al-Shabab was likely to be adopted at the summit.
"There is definitely going to be an offensive message from this summit, definitely an increase in troops and possibly a change in mandate," he said.
"The question is whether this is going to bring Somalia back to some sort of peace after two decades of mayhem."
Guinea and Djibouti announced a plan on Friday to send troopsto bolster the AU peacekeeping force charged with protecting the transitional government in Somalia.
Yoweri Museveni, the Ugandan president, urged African leaders to defeat "the terrorists" and "sweep them out of Africa" during his address.
Mutharika joined him in condemning the perpetrators of the Kampala blasts "in the strongest terms".
"The African Union stands with you, my brother President [Museveni] and with the people of Uganda," Mutharika said.
Al-Shabab said that the attacks were in response to the deaths of Somali civilians at the hands of AU peacekeepers.
The group, which the US says is allied to al-Qaeda, has warned of further violence in Uganda and Burundi unless they pull their troops out of Somalia.