Mali's new leader, Dioncounda Traore, has threatened a "total war" against separatist rebels in the north.
Mr Traore's inauguration marks a return to civilian rule following last month's coup in the West African state.
Mr Traore now has 40 days to organise elections - though correspondents say this deadline is unlikely to be met because of the situation in the north.
Since the coup, Tuareg and Islamist militants have taken control of much of the northern desert region.
The UN says there are continuing reports of civilians being killed, robbed, raped and forced to flee northern rebel-held areas.
"Reports also suggest that tensions between different ethnic groups are being stirred up, increasing the risk of sectarian violence," the UN human rights commissioner Navi Pillay said in a statement.
Mali's former parliamentary speaker was sworn in by Supreme Court President Nouhoum Tapily at a brief ceremony in the capital, Bamako.
Moments after taking the presidential oath and to applause, Mr Traore warned he would use military force to wrest back the northern part of Mali unless Tuareg rebels and Islamist militants ceded control of the territory they seized in the wake of the coup.
He called on the rebels to "return to the fold and to strengthen this nation instead of dividing it," adding that if they do not, "we will not hesitate to wage a total and relentless war."
The BBC's West African correspondent Thomas Fessy in Bamako said there was a standing ovation when coup leader Capt Amadou Sanogo shook hands with the new president.
Correspondents say that while Mr Traore's inauguration may bring hope, lasting peace in the north will not be achieved until the end of the political uncertainty in Bamako - and the role of coup leader Capt Sanogo becomes clear.
West African states lifted sanctions against Mali after Capt Sanogo agreed to step aside in a deal agreed with the regional bloc Ecowas on Friday.
But Capt Sanogo told the BBC subsequently: "The agreement is clear. [Traore] will be here for 40 days and after 40 days, my committee and Ecowas will sit together and fix transition organs."
Asked if that meant he would be back in power after that time, he replied: "I didn't say that. I don't know."
Food crisis warning
Before the deal he had formally asked Ecowas for help in defeating Tuareg separatists and their Islamist allies.
However, he has since said he needs only equipment and logistical support - and rejected the intervention of a 3,000-strong foreign force.
Nevertheless, Ecowas is still mulling the possibility of sending in regional troops, and foreign ministers are discussing the situation on Thursday in Ivory Coast's main city, Abidjan.
The Tuaregs, who inhabit the Sahara Desert in Mali and several neighbouring countries, have fought several rebellions over the years, claiming they have been ignored by Bamako.
But human rights groups warn there could be a major humanitarian disaster in the wake of the fighting in the north.
"The urgency of the situation in Mali is exacerbating an already extremely serious humanitarian crisis affecting the whole of the Sahel region, and the country may soon be plunged into a devastating food crisis with a risk of other shortages, including medical supplies, if the insurrections and insecurity persist," Ms Pillay said.
Correspondents say Mr Traore, 70, has long harboured presidential ambitions - but he had hoped to come to power through the ballot box, by contesting elections originally scheduled for later this month.
The former mathematician heads Mali's largest political party, the Alliance for Democracy in Mali, and was an ally of the deposed President Amadou Toumani Toure, who formally resigned on Sunday.
Known as ATT, the former president had been due to step down this month after two terms in office - and people had become increasingly frustrated with his government for doing little to tackle corruption and the growing insecurity and eventual rebellion in the north.
As a consequence, many Malians are wary of Mr Traore, Bamako-based journalist Martin Vogl told the BBC's Network Africa programme.
Mr Traore is not regarded as charismatic, nor seen by many people as a natural leader, he says.