Arabic language daily El Khabar said the official, named in media reports as Chouib Woustache, opened fire after confronting Tounsi over reports the chief was planning to sack him.
The reports were corroborated by Kamel Mansari, a journalist based in Algiers, who told Al Jazeera that the attacker - the chief commander of the police air division - had been dismissed by Tounsi a day earlier after weeks of disagreement.
Mansari said police checkpoints had sprung up around Algiers following the incident.
He also said rumours had been circulating in Algiers recently that Tounsi was about to be dismissed by the president.
Several newspapers said an inquiry ordered by Tounsi into bribery allegations involving helicopter parts suppliers had implicated Woustache.
"The perpetrator did not accept the conclusions of this inquiry," the Arabic-language Echorouk daily said in its online edition.
"He wasn't ready to submit to any administrative sanction or be subjected to prosecution. He acted after getting wind that he was about to be fired."
The El Watan daily said on its website that the disgruntled official also fired on other colleagues present at the meeting, but there has been no official confirmation of this.
Yazid Zerhouni, Algeria's interior minister, paid tribute to the "fiery patriotism" of Tounsi, who took the job in 1994 when Algeria was battling anti-government Islamist fighters.
"Tounsi gave his whole life to the service of his nation, to the anti-terrorist campaign over the past 16 years and to the modernisation of national security," the minister said.