"The process of NATO enlargement will continue, with due caution but also with a clear purpose - to help create a stable, undivided Europe," he said in a speech at Tbilisi State University.
Russia has adamantly opposed NATO membership for Georgia, whose location straddling a key westward energy route for Caspian and Central Asian oil and gas supplies gives it outsized geopolitical importance.
The NATO chief underlined that the alliance makes it own decisions.
"No other country will have a veto over that process, nor will we allow our strong ties to Georgia to be broken by outside military intervention and pressure," de Hoop Scheffer said. "Georgia has a rightful place in this Europe."
De Hoop Scheffer came to Georgia with the NATO ambassadors of all 26 allies. On Tuesday, the entire delegation visited Gori, a city targeted by Russian bombs and tanks during the war, which now houses a large tent camp for displaced people. The NATO delegation also toured the base of a Georgian brigade that was bombed.
De Hoop Scheffer condemned Russia's recognition of separatist South Ossetia and Abkhazia as independent nations, saying Georgia's sovereignty and territorial integrity must be respected. He also called on Moscow to tone down its rhetoric.
He said NATO still wants to work with Russia, but had put some ties on hold until Moscow complies with an EU-brokered cease-fire and withdraws forces to positions held before the war erupted Aug. 7.
"Punishing Russia is not the way forward. The way forward, really, is to help Georgia," he said.
The alliance in April declined to grant Georgia a Membership Action Plan - a key step toward membership - but assured the nation that it will eventually join.
"While all 26 allies agree that Georgia will one day be a member of the alliance, there are differing views on how fast Georgia should be admitted," he said.
Washington has supported Georgia's entry, but other nations including France and Germany balked in April, wary of Russian ire because of Europe's dependence on Russian energy supplies.
The brief but intense war with Russia has damaged President Mikhail Saakashvili's standing in Georgia - with some residents questioning the wisdom of the Aug. 7 offensive against South Ossetia. Saakashvili claims Georgia was responding to Russian aggression.
De Hoop Scheffer also met Tuesday with parliament speaker David Bakradze - a Saakashvili ally - who said while the governing party faces strong opposition, the country was united in its desire to join NATO and integrate with the West.
Russian tanks, troops and warplanes immediately repelled Georgia's Aug. 7 attempt to regain control of South Ossetia. Russian troops then drove deep into Georgia in a five-day war that killed hundreds of people and displaced nearly 200,000.
Russia has pledged to withdraw forces from Georgian territory outside South Ossetia and Abkhazia within 10 days of the deployment of EU monitors, expected to be in place by Oct. 1.
But Moscow has said it will maintain nearly 8,000 troops in South Ossetia and Abkhazia for the foreseeable future - a plan the United States and EU nations say violates Russia's commitment to withdraw to pre-conflict positions.