“The removal of this al-Qaeda senior leader will disrupt the terrorist organisation’s ability to further plot and carry out global attacks threatening US citizens, our partners, and innocent civilians,” Major Rigsbee said in a written statement.
The strike comes just two days after a US outpost in southern Syria was attacked.
Mr Rigsbee did not confirm whether the US drone strike was carried out in retaliation.
The official statement also claims there was no indication of civilian casualties after the drone strike.
“Al-Qaeda continues to present a threat to America and our allies,” Major Rigsbee continued.
“Al-Qaeda uses Syria as a safe haven to rebuild, coordinate with external affiliates, and plan external operations.
“Al-Qaeda also uses Syria as a base for threats reaching into Syria, Iraq and beyond.”
In its first official death toll since 2014, the UN has reported at least 350,209 people have been killed during the 10 years of war in Syria.
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“Based on initial reports, the attack utilized both unmanned aerial systems and indirect fire,” he said.
“We maintain the inherent right of self-defence and will respond at a time and place of our choosing.”
Al-Tanf, a military base, is the only position with a significant US military presence in Syria outside the Kurdish-controlled north.
American troops were first deployed there when Islamic State fighters controlled eastern Syria bordering Iraq.
Since the militants were driven out, it is seen as part of the larger US strategy to contain Iran’s military reach in the region.