Russia was watching the trip with suspicion, and a top Russian security official accused Cheney of an ulterior motive: seeking to secure energy supplies in the South Caucasus in exchange for U.S. support.
Cheney met with U.S. Embassy officials and international oil executives before going to Azerbaijani President Ilham Aliev's residence on the Caspian Sea.
Cheney said the principle of territorial integrity was endangered today, noting that they were meeting "in the shadow of the Russian invasion of Georgia."
He added that U.S. President George W. Bush had sent him with a clear message that the United States had a "deep and abiding interest" in the stability and security of countries in the region.
Azerbaijan has some of the largest oil and gas reserves in the former Soviet Union.
The U.S. vice president later was to go to neighboring Georgia, where Washington is trying strengthen support for President Mikhail Saakashvili's U.S.-allied government, battered by last month's short war with Russia.
Cheney was expected to announce Wednesday ato help the pro-Western former Soviet republic rebuild after Russia's invasion last month.
CBS News producer Alexsei Kuznetsov said Medvedev made the comments in an interview with Italian TV network RAI, aired widely across Russia.
Medvedev's remarks were a response to a question about whether Russia would agree to take part in a mediating conference in Rome, which Saakashvili has agreed to attend
Despite the inflammatory remarks, Medvedev said Russia was willing "to discuss various issues, including those related to post-conflict settlement in this region, including at international floors."
Medvedev said other Baltic states' concerns about their security in the wake of Russia's operations in Georgia were unwarranted, reported Kuznetsov.
"Their concerns about Russia's policy following the Georgia conflict are only a way to keep the political elite in a somewhat exalted state," he told RAI.
Cheney also planned to visit Ukraine, whose Western-leaning governing coalition has been plagued in infighting and growing wariness about Russia's intentions.
The head of Russia's powerful presidential Security Council criticized Cheney's planned tour, saying his real goal was to trade U.S. support for energy supplies in the region, and to make sure these countries had governments sympathetic to Washington.
"Cheney, during his visits to Georgia, Azerbaijan and Ukraine, will try to instill in them confidence that they will receive support of the U.S., and (he) will do it in such a way that the U.S. will continue to wield influence on them," Nikolai Patrushev said during a visit to neighboring Armenia.
Russia's relations with Washington have become increasingly tense. Since the war in Georgia, Russia has boldly asserted its right to exert clout over what it says is its historic sphere of influence - including many former Soviet republics.
Russia has also objected strongly to U.S. plans to place components of a missile defense shield in Poland and the Czech Republic - both former Soviet satellites - as well as to Western support for Kosovo's independence from traditional ally Serbia.
Both Georgia and Ukraine have sought to pull themselves out from under Russia's shadow, pushing for membership in Western structures such as the European Union and NATO - much to Moscow's consternation.
Washington also has courted Azerbaijan, trying to ensure its oil wealth is exported to the West bypassing Russia. Many European capitals are wary of Russia and its vast oil and gas wealth after disruptions in European-bound Russian gas and oil shipments exported via other former Soviet republics.
The U.S. Embassy in Baku said in a statement that Cheney on Wednesday met with local representatives of British Petroleum and Chevron who briefed him on their "assessments of the energy situation in Azerbaijan and the broader Caspian region - especially in light of Russia's recent military actions in Georgia."
Azerbaijan's government has often been criticized by rights groups for heavy-handed treatment of independent media and opposition groups. International observers have said past elections were flawed.