Judy Ansley said "On Georgia, they talked about the risk of escalation in the region because of the Russian provocations since April, and talked about ways that they could work together to reduce tensions in the region."
Long-running tensions between Russia and Georgia have heightened in recent months over Moscow's support for Georgia's breakaway regions of Abkhazia and South Ossetia, and Tbilisi's drive for NATO membership.
In the latest development, Georgia and the UN accused Russia of shooting down an unmanned reconnaissance plane over Abkhazia in April.
The talks between Bush, who is on a farewell tour of Europe before stepping down as president in January, and Chancellor Angela Merkel, focused on climate change, Afghanistan, and Iran.
Merkel signaled her support for tougher sanctions against Iran, over its refusal to suspend uranium enrichment.
At a press conference following the meeting, Bush said on Iran that "all options are on the table," and reiterated Washington does not rule out military action.
Bush is due to meet with Italian Prime Minister Silvio Berlusconi on Thursday and Pope Benedict XVI on Friday.