International experts say at least 200,000 people have died in Sudan's western Darfur region, while al-Bashir's government says 10,000 have died.
'Sense of infamy'
Most of the deaths have been caused by fighting, but hunger and disease have taken their toll, prompting aid agencies to step in and provide humanitarian aid.
Clinton said al-Bashir's government had now assumed "an even greater sense of responsibility and infamy in the eyes of the world".
She called on governments supporting him to push for the return of the aid workers, or fill the gaps themselves.
"They must replace with money and personnel those who have been expelled so that innocent lives are not lost and further undermined," Clinton said.
The call came as Barack Obama, the US president, announced the appointment of Scott Gration, a retired air force general, as his special envoy to Sudan.
"He's someone with deep experience in the region, who has personal and professional relationships with key leaders and most importantly has a close personal friendship with the president and has his ear," an Obama administration official said.
Gration was often seen with Obama on the presidential campaign trail last year. They got to know each other when Obama visited Africa in 2006 while still a senator.
The US is trying to convince the Arab League, the African Union and others, such as China with influence over Sudan, to press al-Bashir to reverse course, Robert Wood, a state department spokesman, said.
In a meeting last week with Yang Jiechi, the Chinese foreign minister, Obama expressed his "deep concern" about the unfolding humanitarian crisis in Darfur and asked Beijing to put pressure on Sudan's government.
Many African and Arab governments say the ICC's move was counter-productive and hypocritical as it failed to tackle alleged war crimes by Israel against Arabs, or by the United States in Iraq and Afghanistan.
The US, while not a member of the court, supported the decision to indict al-Bashir, who is accused of seven counts of war crimes and crimes against humanity but not for genocide.