The first US ship carrying aid arrived in Batumi earlier this week
The US military has steered a vessel carrying aid to war-torn Georgia away from its expected destination of Poti, a Georgian port occupied by Russia.
The ship instead docked in Batumi, another Black Sea port away from the self-imposed Russian zone of influence.
In a BBC interview, Russian President Dmitry Medvedev accused the US of taking weapons into Georgia under the guise of humanitarian aid.
The Pentagon denied the charge. It gave no reason for docking in Batumi.
Mr Medvedev said ships carrying humanitarian aid were free to dock in Poti, and denied that Russia had a blockade on the port.
"The Americans call them humanitarian loads but it's of course weapons," he said.
Meanwhile, UK Foreign Minister David Miliband is in Ukraine trying to put pressure on Moscow, a day after Russia's decision to recognise the independence of Georgia's breakaway provinces of South Ossetia and Abkhazia.
The two regions have had autonomy since a civil war in the early 1990s, but no other nation has recognised their independence.
A conflict broke out earlier this month when Georgia tried to reimpose its authority in South Ossetia, sparking retaliation from Moscow.
The US and other Western governments have backed Tbilisi in their struggle with Moscow, and the US Coast Guard cutter Dallas is the second navy ship to arrive carrying aid since the conflict began.
The BBC's Gabriel Gatehouse, in Tbilisi, says that by choosing to dock in Batumi, the US appears to have shied away from a possible confrontation with Russian troops in Poti.