US officials said the incident showed Russia’s aggressive and risky behavior and pledged to continue their surveillance.
However defence chiefs of both countries - Lloyd Austin of the US and Sergei Shoigu of Russia - spoke over the phone.
Russia has long voiced concern about US surveillance flights near its borders, but Tuesday’s incident left tensions soaring between the two nuclear powers.
Nikolai Patrushev, the secretary of Russia’s Security Council, said in televised remarks the drone incident was “another confirmation” of direct US involvement in the Ukraine conflict.
The Kremlin has repeatedly said the United States and other Nato members have become direct war participants by supplying weapons and intelligence to the Kyiv government and pressuring it not to negotiate peace.
US officials said Russia has dispatched ships to try to recover the wreckage.
US National Security Council spokesperson John Kirby said the MQ-9 Reaper drone was in international airspace when a Russian fighter jet struck its propeller.
US officials accused Russia of trying to intercept the unmanned aerial vehicle, although its presence over the Black Sea - a strategic military and economic area for both Russia and Ukraine - was not uncommon.
“It is also not uncommon for the Russians to try to intercept them,” Mr Kirby said, adding that such an encounter “does increase the risk of miscalculations, misunderstandings.”
Kirby said the US “took steps to protect the information and to protect, to minimise any effort by anybody else to exploit that drone for useful content.”
Sergei Naryshkin, the head of Russia’s Foreign Intelligence Service, said Russia has the technological capability to recover the drone’s fragments.
Kremlin spokesman Dmitry Peskov repeated the Defense Ministry’s statement that Russian jets didn’t use their weapons or impact the US drone.
In Washington, Russian Ambassador Anatoly Antonov expressed concern about “the unacceptable actions of the US military in the close proximity to our borders.”
“What do they do thousands of miles away from the United States?” he said in remarks the Russian Embassy released on Wednesday.
“The answer is obvious - they gather intelligence which is later used by the Kyiv regime to attack our armed forces and territory.”
He noted that “it is important that the lines of communication should remain open,” emphasising that “Russia does not seek confrontation and stands for pragmatic cooperation in the interests of the peoples of our countries.”
US Defence Secretary Lloyd Austin said the Russian intercept was part of a “pattern of aggressive, risky and unsafe actions by Russian pilots in international airspace.” He said Russia must operate its aircraft in a safe manner.
“Make no mistake, the United States will continue to fly and to operate wherever international law allows,” Mr Austin said in remarks before a virtual meeting of a US-led effort to coordinate Western military support for Ukraine.
While encounters between Russian and NATO aircraft are not unusual, the war has heightened the significance and potential hazards of such incidents.
“The last thing that anybody should want is for this war in Ukraine to escalate to become something between the United States and Russia,” Mr Kirby told CNN on Wednesday.
“We’ve been working very, very hard throughout the beginning of this conflict ... to make sure that it doesn’t escalate,” he added.
Meanwhile, the UK Defense Ministry said British and German air force fighter jets were scrambled on Tuesday to intercept a Russian aircraft near Estonian airspace. The UK and Germany are conducting joint air policing missions in Estonia as part of Nato’s bolstering of its eastern flank.
The ministry said the Typhoon jets responded after a Russian air-to-air refueling aircraft failed to communicate with Estonian air traffic control. The Russian plane did not enter the airspace of Estonia, a Nato member.
In Ukraine, at least three civilians were killed and another 23 wounded in Russian strikes over the previous 24 hours, Ukraine’s presidential office said.
In the northeastern Kharkiv region, one person was killed and another was wounded in Vovchansk, a city near the border with Russia.
In the south, Russian forces shelled the city of Kherson seven times in the last 24 hours, hitting an infrastructure facility and residential buildings and wounding four people.
In Dnipropetrovsk province, Russian forces shelled Nikopol and Marhanets, towns located across a river from the shut-down Zaporizhzhia Nuclear Power Plant.