The car bomb on Wednesday targeted dozens of potential recruits lined up to register at the academy in the centre of the Yemeni capital.
"This cowardly criminal action reflects the bloodthirsty and savage character of elements belonging to the terrorist Al-Qaeda organisation," the Supreme Security Committee said in a statement published by the official Saba news agency.
Al-Qaeda in the Arabian Peninsula (AQAP), the jihadist network's powerful affiliate in Yemen, has claimed responsibility for previous attacks on security forces.
But a leader of Al-Qaeda in Yemen, Sheikh Saleh Abdel Ilah al-Dahab, denied any involvement by the militant group in Wednesday's attack.
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"Al-Qaeda has nothing to do with the incident," he wrote on Twitter, accusing the Shiite Huthi militia that overran Sanaa in September of being behind the bombing.
A Huthi statement on Wednesday denounced the attack as a "despicable crime," vowing its perpetrators "will not go unpunished".
Unstable and impoverished Yemen has been hit by a wave of violence in recent months, as the Huthis clash with Sunni tribal forces and Al-Qaeda militants.
The interior ministry gave the new toll on Thursday, after police earlier said 37 people had died in the attack, which was condemned by the United States, the European Union and the United Nations.
The ministry said 71 people had also been wounded.