It was not immediately clear who carried out the attack by air and sea drones about 110 km off the coastal town of Byala in eastern Bulgaria on Tuesday, but there are growing concerns about hybrid attacks by Russia as it wages war in Ukraine.
Shipping sources said it appeared to be the first such attack in the waters of Bulgaria's exclusive economic zone.
Radev said it was unclear whether the drones came from Russia or from Ukraine, the BTA news agency reported. Bulgaria does not border either country but it holds a strategic position in the Black Sea, where both Ukraine and Russia have major ports.
Ukraine's foreign minister blamed Russia for the attack. Moscow has made no comment on the incident.
Two ships were hit in the attack, Radev said in a televised statement. The crew of one, which was carrying grain, was rescued, with two injured. The other, which sank, was a Togo-flagged ship whose cargo was not disclosed. It is unclear how many people were on board.
The incident occurred some 140 nautical miles away from the Ukrainian coast.
A search has been launched for the missing crew and for any signs of an environmental threat.
A maritime security source said initial assessments of the strike suggested it had probably been a Russian attack.
Radev did not say who was behind the attack but made a reference to Russia's war in Ukraine.
"If this war is not brought to an end in time, it will continue to expand its geographical scope and increase the risk of even a global conflict," he said.
"We are seeing the war intensify, with all the rules of international law now being violated, and civilian vessels being attacked at sea. This is absolutely unacceptable."
European Commission President Ursula von der Leyen also condemned the attack, saying: "Commercial ships - and innocent crews - are being targeted, with lives already lost at sea."
Ukraine's Foreign Minister Andrii Sybiha said in a post on X that Russia was creating "a dangerous chain of consequences" through attacks on civilian shipping.
"By attacking civilian ships, it makes navigation a challenge. By making navigation a challenge, it drives up risks, insurance and transport costs, and threatens the flow of food to global markets," he wrote.
British maritime risk management group Vanguard said the attacks on Tuesday were on the Togo-flagged general cargo vessel ALFA WATAN and the Palau-flagged general cargo vessel ABLE, within Bulgaria's economic zone.
The drone attack follows an incident in which Romanian authorities said on Monday two people had died in a fire on a ship in the Black Sea outside Romania's territorial waters.
"The attacks represent a significant escalation in the threat to commercial shipping in the western Black Sea," maritime security firm MARISKS said in an advisory in which it advised captains and operators to watch out for drone activity in the area.
"Of particular concern is the apparent geographic expansion of incidents beyond waters immediately adjacent to Ukraine and into the EEZs of NATO members Romania and Bulgaria."
Ukrainian President Volodymyr Zelenskiy blamed Russian drones for the Romania incident. Russian authorities have also made no comment on that incident.
Since Russia's invasion of Ukraine in 2022, European countries have reported Russian drones breaching their airspace multiple times and mines floating in the Black Sea across trade and energy routes.
