Al-Bashir rejects claims that he ordered mass murder, rape and torture in the volatile Darfur region.
EU countries support efforts to bring al-Bashir to justice at the ICC, but want to keep channels of communication open with the controversial leader.
The international community is hoping that a refurendum planned for January in the semi-autonomous south of Sudan will pass without violence, and will seek to maintain dialogue with al-Bashir's administration in the run-up to the poll.
"Diplomats attending al-Bashir's inauguration would be making a mockery of their governments' support for international justice," Elise Keppler, a senior counsel of the International Justice Program at Human Rights Watch, said ahead of the inauguration.
Al-Bashir won the presidential election last month with 68 per cent of the vote after the main opposition candidates pulled out citing electoral fraud.
His party also did well in parliamentary polls, winning more than 95 per cent of the seats available in the north of country. In the south, the former rebels of the Sudan People's Liberation Movement (SPLM) won most of the seats.
The former enemies are now in talks to form a government that would allow South Sudan to hold a refurendum on independence. Observers predict the referendum will see the oil-procuding South secede from the rest of the country.
ICC judges told the UN security council on Wednesday that Sudan was protecting ICC suspects rather than arresting them, a move aimed at increasing pressure on Khartoum.
As well as al-Bashir, former state minister of humanitarian affairs Ahmed Haroun and a militia leader known as Ali Kushayb face ICC arrest warrants.
The southern vote on independence is set for January 9, 2011 and is a key focus of the international community.