BAKU (AFP) - The United States and Russia squared off over the Caucasus and Central Asia on Wednesday as US Vice-President Dick Cheney said Washington had an "abiding" interest in vital regions once dominated by Moscow. Russia and Georgia meanwhile virtually shut down diplomatic exchanges, with Moscow suspending visas for Georgian citizens and saying it would pull troops out of Georgia only when a French-brokered peace plan was fully implemented. Speaking in the oil-rich former Soviet republic of Azerbaijan, Cheney said: "President Bush has sent me here with the clear and simple message for the people of Azerbaijan and the entire region. "The United States has a deep and abiding interest in your well-being and security." Cheney, the most senior US official to visit the Caucasus region since Russia and Georgia fought a brief war last month, said access to energy resources there and in Central Asia was a top concern for Washington. "Energy security is essential to us all and the matter is becoming increasingly urgent," Cheney said after meeting Azerbaijani President Ilham Aliyev. "We must work with Azerbaijan and other countries in the Caucasus and Central Asia on additional routes for energy exports," he said. US officials simultaneously announced a one billion-dollar aid package for Georgia following the conflict with Russia. Cheney's comments came a day after Russian Prime Minister Vladimir Putin sealed a new gas pipeline deal in Uzbekistan. There was a clear signal that Washington did not intend to allow Moscow to regain the unchallenged control over the politics and natural resources of the Caucasus and Central Asian regions. Cheney was due to travel Thursday to Georgia for a meeting with that country's beleaguered, US-backed President Mikheil Saakashvili, a leader that Russian President Dmitry Medvedev referred to Monday as a "political corpse." Russia and Georgia meanwhile closed down diplomatic exchanges, though the parliament in Tbilisi formally lifted the state of war in most of the country that was declared when the hostilities broke out last month. "The Russian embassy in Georgia is no longer functioning. The consular section is closed as well, pending future directives from Moscow," embassy spokesman Alexander Savonov told AFP in Tbilisi. In Moscow, Georgia's charge d'affaires Givi Shugarov told Interfax news agency that his embassy had also ceased diplomatic functions though the consulate was still working to serve Georgians living in Russia. Russia's foreign Ministry said it had stopped issuing visas to Georgian citizens. Russia's President Dmitry Medvedev will seek backing for his country's intervention at a Moscow summit of seven ex-Soviet states on Friday (tomorrow). Russia hopes the meeting of the Collective Security Treaty Organisation - Armenia, Belarus, Kyrgyzstan, Kazakhstan, Russia, Tajikistan and Uzbekistan - will build on another gathering in Central Asia last week that included China, said presidential advisor Sergei Prikhodko. "We expect from our partners... confirmation of understanding and a principled assessment of Georgia's actions, which led to this crisis," Prikhodko said, according to the RIA Novosti agency. Medvedev and French President Nicolas Sarkozy spoke by telephone Wednesday ahead of a meeting between the two next week to discuss Georgia. Medvedev told Sarkozy he welcomed the "balanced decision" taken by EU leaders at a summit this week but said the final document did not "pass judgement on Georgia's aggressive actions," the Kremlin said in a statement.