Dan gave no indication of where the unmanned aerial vehicle had come from, saying an investigation into the incident was underway.
A military source told the Reuters news agency that the drone's origin was still being established, "but in this part of the world it is Russia that is the attacker."
Writing on X, Dan said the F-16 was flown by a Romanian pilot and that teams were combing the site to establish further details.
He added that the area was unpopulated, meaning the pilot could engage without endangering anyone on the ground.
The president's statement came around the same time an air raid alert was sounded in the Ukrainian capital Kyiv over a Russian attack.
Romania's defence ministry said the drone was destroyed by a missile fired near Padina in the east of the country.
Debris landed in a wheat field, with no damage or injuries reported, according to a local official.
Radar first detected the object near Sulina, on the Black Sea coast close to the border with Ukraine, before it crossed into Romanian airspace.
Fighter jets were then scrambled, including two Italian Eurofighters stationed in Romania under NATO's air policing mission, according to Reuters.
Acting Defence Minister Radu-Dinel Miruta praised the air force in a Facebook post, saying investment in defence was paying off.
Romania shares a 650 km border with Ukraine and has recorded repeated airspace violations by drones since Russia's full-scale invasion in 2022, when Moscow began targeting Ukrainian river ports along the Danube.
Similar incursions have also been reported in Poland and the Baltic states.
Romania passed a law in 2025 setting out legal grounds for intercepting or downing drones.
The rules were applied for the first time during Friday's incursion.
One of the most serious such incidents in Romania occurred in late May, when a drone struck an apartment building in Galați, near the Ukrainian border, injuring two people.
(ał/gs)
Source: PAP, Reuters