Gration, who is expected to visit Darfur over the weekend, met Mutrif Siddiq, a senior foreign ministry official, on Thursday and could possibly meet al-Bashir.
"The US embassy told us clearly that [Gration] was here to listen. We don't expect him to come with a plan," Ali Sadiq, Sudan's foreign ministry spokesman, told the AFP news agency.
Aid groups expelled
Al-Bashir expelled 13 international aid groups from Darfur after the ICC issued the warrant, prompting a warning by Hillary Clinton, the US sceretary of state, that he would be held responsible for "every single death" in places where the agencies were operating.
Barack Obama, the US president, has said Gration would try to kickstart talks between rebels and the government in order to end the Darfur conflict.
Speaking after meeting Gration on Monday, he said he hoped to find a way for humanitarian workers to resume their work in Darfur.
"We have to figure out a mechanism to get those NGOs back in place, to reverse that decision, or to find some mechanism whereby we avert an enormous humanitarian crisis," Obama said.
More than 2.7 million people driven from their homes by the civil war in Darfur receive food and medical care from the aid agencies, which also provide water.
|Al-Bashir has visited African and Arab states in defiance of the arrest warrant [AFP]
Sadiq, the Sudanese spokesman, said the US and Khartoum should work together.
"We need to talk about the humanitarian situation in Darfur, to make sure that the United States and Sudan work together ... to make sure that people are not affected," he said.
"Sudan recognises the United States as being a very important country in the world and Sudan, like many other countries, will always want to maintain very good and normal relations with the Unites States."
Al-Bashir has visited several countries since the arrest warrant was issued and remains defiant about his government's decision to expel the aid agencies.
"In one year we will Sudanise all the aid on the ground and we can fill the gap in food distribution within one year because the Sudanese Red Crescent already distributes 45 per cent of the food in Darfur," al-Bashir said during a visit to Saudi Arabia on Wednesday.
At least 300,000 lives have been lost in Darfur since 2003, when the conflict began.
Sudan puts the death toll from the six-year war at only 10,000.
In February, the Sudanese government and the rebel Justice and Equality Movement signed an agreement in Doha, Qatar, aimed at holding peace talks, but the Jem threatened to back out if Khartoum does not allow the aid agencies back in.