Russian media reported that the servicemember was offered Ukrainian citizenship and money by Ukraine's Security Service.
Russia had declared that any ships traveling to Ukraine's Black Sea ports would be seen as possibly carrying military cargoes.
This is the 43rd security assistance package approved by the United States for Ukraine. More than $43 billion in US military aid has been provided since Russia's invasion in 2022.
"We agree with the US assessment that this is a coordinated effort to justify and lay blame on Ukraine for any attacks against civilian ships in the Black Sea," Woodward told reporters.
Since Russia quit the deal and began attacking Ukrainian food-exporting ports on the Black Sea and Danube river, global wheat and corn futures have risen sharply.
"The crew of the Ivanovets missile boat carried out live firing of anti-ship cruise missiles at a target vessel..." the Defense Ministry said in a statement.
"All ships proceeding to Ukrainian ports in Black Sea waters will be considered as potential carriers of military cargo," the Russian Defense Ministry stated.
Russia's defense ministry said it had struck Odesa, where the Ukrainian navy has its headquarters, and Mykolaiv, near Ukraine's Black Sea coast.
At the time of the attack, a US RQ-4 Global Hawk unmanned surveillance aircraft was in the central area of the Black Sea, the defense ministry said.