Mr Bashir visited UN peacekeepers in Darfur last week
South Africa and Libya are pushing the UN to suspend accusations against Sudan's president, linking the issue to a Darfur peacekeeping mandate.
Divisions emerged as the Security Council discussed extending the mandate of a joint African Union-UN mission to Darfur, which expires on Thursday.
South Africa and Libya want to include a clause delaying any charges against Sudanese President Omar al-Bashir.
The International Criminal Court has accused Mr Bashir of war crimes.
"We have a division in the council at this point," US Ambassador Zalmay Khalilzad told reporters at the UN.
South Africa and Libya are backed by China and Russia in seeking a 12-month delay to the moves against Mr Bashir.
Under the Rome Statute setting up the ICC, the UN Security Council has the powers to defer charges by 12 months.
But EU countries have said they have not seen anything in the behaviour of Khartoum that would warrant such a move.
Mr Khalilzad said linking the mandate to the ICC accusations was "premature" and "unwarranted".
The BBC's Vikou Bessan at the UN said a failure to renew the peacekeeping mandate would result in a legal vacuum, and one possibility would be to extend the mandate for a month while negotiations over the ICC accusations continue.
ICC Chief Prosecutor Luis Moreno-Ocampo sought an arrest warrant against Mr Bashir earlier this month, over his alleged role in Sudan's western Darfur region.
He accused Sudan's leader of running a campaign of genocide that killed 35,000 people outright, at least another 100,000 through a "slow death" and forced 2.5 million to flee their homes in Darfur.
Mr Bashir has said he is not worried by the accusations.
ACCUSATIONS AGAINST BASHIR
Killing members of the Fur, Masalit and Zaghawa ethnic groups
Causing these groups serious bodily or mental harm
Inflicting conditions of life calculated to bring about these groups' physical destruction
Crimes against humanity:
Attacks on civilians in Darfur
Pillaging towns and villages
His government has denied mobilising the Janjaweed militias, accused of widespread atrocities against Darfur's black African population.
The Sudanese ambassador to the UN, Abdalmahmood Abdalhaleem Mohamad, said a suspension of the possible charges would not entirely satisfy Sudan.
"Our feeling is to do away once and for all with this unfair, unjust and politically motivated decision," he said.
Mr Mohamad called the accusations against Mr Bashir an "affront to Africa" and said Sudan was being unfairly singled out by Mr Moreno-Ocampo.
"He is a screwdriver in the workshop of double standards," he said.
Judges are expected to make a decision on Mr Moreno-Ocampo arrest warrant request in the coming months.
The African Union has called for the UN Security Council to suspend the accusations, while the Arab League has warned they set a dangerous precedent.
On Monday, a group of mainly African relief and advocacy groups said the AU-UN force in Darfur was failing to protect civilians because it was too small and inadequately funded.
Only about a third of the intended 26,000 peacekeepers have been deployed.
The UN estimates that five years of conflict in Darfur have left 300,000 people dead and more than 2 million people homeless.