"[South Stream] is strategically important for [all of] Europe," Miller said in a statement Sunday. "[This] new trans-European gas transmission system will eliminate the pressing problem of transit risks and secure uninterrupted Russian gas supplies to dozens of thousands of European consumers."
Miller's comments came as engineers welded the first joint of the Serbian section of the pipeline.
South Stream, designed to have an annual capacity of 2.2 trillion cubic feet of natural gas, adds a layer of diversity to a European market that depends largely on Ukraine as a major transit hub for Russian energy supplies.
A 2009 contract dispute with Kiev prompted Gazprom to cut gas supplies through Ukraine, leaving downstream consumers in the cold for several weeks.
"South Stream will adjust the European energy map for the better, becoming an integral part of the EU's energy security system," Miller said.
Hungary is next in line for pipeline construction, which started in Bulgaria in late October.
South Stream is expected to begin service in 2015.