A prosecutor said he had opened an investigation into the disaster when several thousand youths descended on the Michel d'Ornano stadium on Monday night hoping for one of 1,500 army posts.
Security officials said the dead were left after people tried to push through one gate.
They said some tried to force the gate open while others tried to jump over a wall into the stadium.
The government revised down a toll of 37 dead to 31 but officials said many of the 145 injured were in serious condition.
A 24-year-old man, who declined to be named, told AFP how people were pushing to get through the gate, sparking a stampede. "There were people injured far worse than me," said the survivor, who dislocated his foot.
Another survivor, who also requested anonymity, said: "There was a row of people in front of me. The people fell. I fell on top of them and other friends fell on top of us."
He said he lost conscious and only woke up in an ambulance.
Several videos on social media appeared to show dozens of bodies in a city morgue.
Others showed injured people being admitted to hospitals in Brazzaville.
The army said in a statement read on national television that the recruiting drive had been indefinitely suspended.
Tresor Nzila, head of local rights NGO, called for a full investigation and to hold the Congolese government responsible for not evaluating the risks of a call-up.
"The Congolese government is incapable of creating other employment opportunities," he said. "The defence and security forces have become the main job providers".
The Republic of Congo, which is also known as Congo-Brazzaville to distinguish it from its larger neighbour the Democratic Republic of Congo, is an impoverished country of about five million people -- despite its rich oil and gas reserves.
Youth unemployment is about 42 percent, according to the World Bank.
Congo-Brazzaville's state prosecutor Andre Ngakala Oko said he had launched an investigation.
Congo has witnessed similar disasters. Seven people died in a stampede at a music festival in Brazzaville in 2011.
And at least 150 people were trampled to death in the capital in 1994 when worshippers crammed into a church to avoid a storm.
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