"NATO strongly supports the sovereignty and territorial integrity of Bosnia and Herzegovina," said Geoana.
"Secessionist policies and divisive rhetoric undermined stability and hamper reforms and the well-being of your people," he added in a statement.
Bosnia-Herzegovina has in recent years faced frequent threats from the Bosnian Serb political leader Milorad Dodik, who heads the Republika Srpska (RS).
Dodik has several times called for secession from Bosnia, which has earned him sanctions from the United States and Britain.
Dodik, who maintains close relations with Russian President Vladimir Putin, has nevertheless repeatedly insisted that Bosnia is heading towards "peaceful separation".
Geoana said the security situation in Bosnia and Herzegovina was the topic of the talks during his two-day visit there, "because what happens in Bosnia and Herzegovina matters for the security in the Western Balkans.
"And what happens in the Western Balkans matters for all of us in Europe."
NATO headquarters in Sarajevo will "continue to coordinate" its support with the European Union-led operation Althea (EUFOR) peacekeeping force, he added.
Since the beginning of the Russian invasion of Ukraine in February 2022, EUFOR has enlarged its presence in Bosnia, from 500 to 1,100 troops.
Bosnia was torn apart by a bloody inter-ethnical war in the 1990s that killed 100,000 people.
Today, it is a country divided into two entities: Serb, in favour of the country's military neutrality, and Bosnian-Croat, whose leaders want the country to join NATO.
This stand-off is effectively blocking the country's accession to the Alliance, as decisions on defence have to be taken unanimously by the country's tripartite presidency: Bosnian, Croat and Serb.
The Serb member of the presidency, Zeljka Cvijanovic, who in principle is not opposed to cooperation with NATO, did not attend the meeting with Geoana and members of the North Atlantic Council.
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