Chad's main opposition parties say the army's appointment of President Idriss Déby's son as the nation's new leader is an "institutional coup".
Déby, 68 - who had been in power for three decades - died after being shot as he battled rebels on the frontline.
The rebels too have objected to the move, saying: "Chad is not a monarchy."
Mahamat Idriss Déby Itno, also known as "General Kaka", was in charge of the presidential guard and is to lead the country for 18 months until elections.
The government and parliament have been dissolved, but constitutional experts say the speaker of parliament should take over when a sitting president dies before organising elections.
Déby's death was announced on state TV on Tuesday - a day after provisional election results projected he would win a sixth term in office at the helm of the oil-rich country that has been at the forefront of regional efforts to fight Islamist militants.
There are fears that the death could trigger political instability in the vast semi-arid country with a long history of rebellions and coup attempts and where the opposition is weak and divided.
An umbrella group of trade unions has joined the opposition to reject the establishment of the Transitional Military Council, calling for dialogue and workers to stay at home until there is a resolution.
Mourning chants amid shock
By Mahamat Adamou, N'Djamena
Downtown N'Djamena is on full alert - with lots of tanks and other armoured vehicles along the perimeter of the presidential palace and parked at key junctions. Others shops and markets in the Chadian capital are open - though not as busy as usual - and people aren't sending their children to school.
People are still in shock here following President Déby's death - even those that opposed him are stunned. The vast majority of the population is under 30 years of age and have never known any other president.
In between programmes, state TV is broadcasting religious mourning chants. Even though some might feel that it is good that Déby's grip on power is no more, there is a sense of sadness that he has gone in this way.
"I am not pleased with the way Idris Déby died, that's not what we wished for him, but we wanted him to leave power. He made us suffer a lot, there's no women's rights in Chad. Until today he did nothing for us," one woman told BBC Afrique.
Another man agreed: "No-one wishes for someone's death in life, it is a shock, but we needed change. By change we didn't mean his son or any military."
The rebels too are adhering to traditional mourning customs, saying they have halted their advance south until after Déby's burial on Friday.
Who is Mahamat Idriss Déby Itno?
He is a 37-year-old four-star general who has played a leading role in the army since 2013 when he was appointed deputy head of Chadian forces taking part in anti-terror operations in Mali.
He is also known as "General Kaka" - a reference to his upbringing as he was raised by President Déby's mother and "kaka" means grandmother in Chadian Arabic.
The late president, who was a Muslim, had a large family, having married several times, and had an unknown number of children.
BBC Monitoring's Africa specialist Sam Murunga says Gen Kaka, who has been appointed president and head of the armed forces, has a reputation for discretion and shunning the limelight, unlike some of his half-brothers.
Although not a known personality, he is said to be greatly respected by the army's rank and file.
It is reported that he was at the frontline in northern Chad when his father was fatally shot.
Why was the president at the front?
Déby was an army officer by training and a former head of the military who came to power in 1990 through an armed uprising - and faced numerous challenges and many coup plots in the years that followed.
Observers say it is no surprise to hear he died on the front as he would often take charge during military confrontations - including at a major battle on Lake Chad against Boko Haram militants last year.
The latest rebel incursion began on election day when Fact (the Front for Change and Concord in Chad) mounted a border attack from Libya.
The group grew out of Chadian rebels once based in Sudan's Darfur region who have mounted various attempts to overthrow Déby, from the Zaghawa ethnic group.
Power struggles in Chad tend to be along ethnic lines and the rebels are known to be dominated by the Gorane community of Déby's predecessor, Hissène Habré - so they are likely to have some backing from his supporters.
In the last few years the fighters have built up their base in Libya in the Tibesti mountains, which straddle northern Chad and part of southern Libya.
How does Déby's death affect the fight against jihadists?
African leaders have expressed dismay at Déby's death as Chadian forces are considered to be the most effective in the fight against Boko Haram militants and other jihadists linked to the Islamic State group and al-Qaeda in the region.
"We don't want a power vacuum," Nigeria's Foreign Minister for Geoffrey Onyeama told BBC Focus on Africa radio.
In a statement, the French presidency described Déby as a "brave friend" and said it affirmed its attachment to the stability of Chad. Over the years, France has deployed troops and fighter jets to push back Déby's opponents.
France's 5,000-strong anti-terror force, called Operation Barkhane, is also based in N'Djamena.
It has been announced that French President Emmanuel Macron intends to attend Déby's funeral.