Sudan, which does not recognise the ICC, rejects the charge.
Susan Rice, the US ambassador to the UN, told the 15-nation council on Friday: "We urge the international community to press the government of Sudan to reverse its expulsion edict and to ensure it does nothing to worsen an already grave situation.
"President Bashir created this crisis," she said. "He should rectify it immediately."
The UK, Austria, Uganda and several other countries have appealed to Khartoum to rethink its position.
Peace talks halted
Sudan has maintained its position despite a rebel group in Darfur saying it was pulling out of peace talks with the Sudanese government after the aid agencies were expelled.
Khalil Ibrahim, the leader of the Justice and Equality Movement (Jem), told the Reuters news agency by telephone on Friday: "The movement cannot negotiate with the government of al-Bashir."
Jem signed a deal with the Sudanese government after talks in the Qatari capital, Doha, last month, under which both sides agreed to undertake "good faith" measures.
"There was supposed to be a conference [in Doha] after three weeks but we will not go," Ibrahim said.
He said the government must allow the expelled aid agencies back into Darfur and free Jem prisoners before talks could resume.
Rashid Khalikov, a senior UN humanitarian affairs official, told the council on Friday there were "significant signs of an erosion of humanitarian response capacity, with a concurrent impact on the lives of people in Darfur" since the 13 foreign and three domestic NGOs were expelled.
UN officials say the banished aid groups accounted for around half of the aid-distribution capacity in Darfur.
|Ibrahim signed a "good faith" deal with Sudan after talks in Qatar last month [EPA]
Sudan says the aid groups, including Oxfam, Save the Children and Care, helped the ICC issue the arrest warrant. The groups reject the charge.
Luis Moreno Ocampo, the ICC's chief prosecutor, who is in New York to urge countries to act on the ICC arrest warrant, told reporters he had received no help or information from NGOs or UN agencies in his investigation.
He said al-Bashir's decision to expel NGOs proved the court had been right to issue a warrant for his arrest.
"Now that he expelled humanitarian assistance, he is confirming he is exterminating his people," Ocampo said.
"That is why his arrest is needed to stop the crimes."
UN officials say that as many as 300,000 people have died in six years of conflict in Darfur between African rebels and the Arab-dominated government. Khartoum says 10,000 have died.