In the first incident, a vehicle exploded as a group of about 30 members of the Yemeni security forces travelled from the town of Loder to the southern city of Aden, the security source said.
"An exchange of fire with Al-Qaeda fighters" followed the blast, the source said, adding that "six of our men were killed and others were wounded" in the ambush.
Separately, about 30 kilometres (18 miles) away, a known Al-Qaeda haunt in the mountains of Khabar Al-Maraqsha was targeted by naval forces operating in the Gulf of Aden, tribal sources said.
There was no immediate confirmation of the report.
The incidents come after an American raid in southern Yemen at the weekend that US military says was "likely" to have killed civilians, in the first such operation authorised by President Donald Trump.
The US military said it lost a Navy SEAL during the land and air strike in the Yakla region of Baida province that had killed 14 members of Al-Qaeda in the Arabian Peninsula.
A Yemeni provincial official had previously said 16 civilians were also killed in Sunday's raid -- eight women and eight children -- but the US military's Central Command did not provide any numbers.
In a report issued today, the International Crisis Group warned that Al-Qaeda could benefit from military actions like the deadly US raid.
"The Yemeni branch of Al-Qaeda is stronger than it has ever been," ICG said.
"The first military actions by the Trump administration in Yemen bode poorly for the prospect of smartly and effectively countering AQAP," read the report.
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