Three suspected militants were killed today in the area of Bouria, 120 kilometres (75 miles) east of Algiers, the ministry said in a statement.
Two Kalashnikovs and a semi-automatic rifle were seized, it added.
The fourth militant were killed in a separate raid on yesterday in the Tiaret region, 340 kilometres southwest of Algiers.
A separate statement from the army today said troops killed a fifth militant in the Tiaret region and that soldiers had also seized an assault rifle in the operation.
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Gourdel was kidnapped on September 21 by Jund al-Khilifa, or "Soldiers of the Caliphate," which has pledged allegiance to the Islamic State group in Iraq and Syria.
The army says close to 80 Islamist militants have been killed since the start of 2014 in Algeria.
The daily Al-Watan newspaper reported that the army had identified five individuals thought to be behind Gourdel's execution, including the militant who conducted the beheading.