TIBLISI, Georgia (CNN) -- U.S. Vice President Dick Cheney said Thursday the United States firmly backs NATO membership for Georgia, telling Georgian President Mikheil Saakashvili that America will help his country rebuild its democracy and economy after last month's conflict with Russia.
Cheney is the highest-level U.S. official to visit Georgia since the crisis with Russia, and he emphasized that the Central Asian nation can count on Washington as a solid ally.
"We will help your people to heal this nation's wounds, to rebuild this economy, and to ensure Georgia's democracy, independence, and further integration with the West," Cheney told Saakashvili in a statement after their meeting.
"In their hearts, the Georgian people have great courage, and in America, they have a sturdy and faithful friend."
Cheney's brief visit to Tbilisi follows Wednesday's announcement by the United States of a $1 billion aid package for Georgia to help with humanitarian aid and reconstruction after last month's conflict with Russia.
The aid package is on top of $30 million in humanitarian assistance which Cheney said the United States has already given to Georgia.
"America will help Georgia rebuild and regain its position as one of the world's fastest-growing economies," Cheney said. Watch Cheney in Georgia »
Saakashvili thanked the United States for standing by Georgia, saying it shows how close the countries are.
"The spirit and will of my nation, the resolve of my government are stronger than ever before," Saakashvili said. "As many challenges lie ahead of us, we are willing to tackle them."
The vice president criticized Russia's military actions in Georgia as an invasion of its sovereign territory and "an illegitimate unilateral attempt" to change Georgia's borders by force. He said Russia's actions have cast "grave doubt" on its intentions and reliability as an international partner.
Cheney also said the United States is committed to Georgia's eventual membership in NATO, promising, "Georgia will be in our alliance."
The Georgia-Russia conflict and the issue of NATO membership are likely to be topics on Cheney's next stop, in Kiev, Ukraine. That country -- which, like Georgia, is a former Soviet republic -- is also seeking NATO membership, something that has angered Russia.
The vice president discussed the conflict Wednesday during his visit to Azerbaijan, but another main topic was energy. Azerbaijan, which borders Georgia and Iran and sits on the Caspian Sea, is an oil- and gas-rich nation and a key U.S. ally in the region. Watch: Cheney meets with President Ilham Aliev »
Cheney met with representatives of energy companies BP and Chevron and held talks with President Ilham Aliyev. He said the United States has a deep interest in maintaining the country's stability and security.
"The United States strongly believes that, together with the nations of Europe, including Turkey, we must work with Azerbaijan and other countries in the Caucasus and Central Asia on additional routes for energy exports that ensure the free flow of resources," Cheney said after his meeting with Aliyev. "Energy security is essential to us all, and the matter is becoming increasingly urgent."
In announcing the Georgia aid package, U.S. Secretary of State Condoleezza Rice emphasized the money is intended for humanitarian aid and reconstruction -- not to rebuild the Georgian armed forces the Russians rolled over in early August. Russian leaders have raised questions about U.S. intentions about providing Georgia with arms.
"This is a reconstruction package for the Georgian economy," Rice said in Washington. "It is not yet time to look at the question of assistance on the military side."
Rice said the biggest share of the aid, $570 million, is to be sent over the next five months. The remaining $430 million will be up to the next administration.
After Georgia and Ukraine, Cheney plans to end his trip in Italy to meet leaders there and discuss the transatlantic alliance.