"It is my firm belief that this conflict cannot be solved militarily," Merkel said after meeting with Hungarian Prime Minister Viktor Orban in Budapest.
She said she prefers economic sanctions as decided by the European Union and negotiations to "solve or at least mitigate the conflict."
Fighting in eastern Ukraine has claimed more than 5,100 lives since April and displaced 900,000 people. Despite a September cease-fire and a period of relative calm in December, the fighting has intensified in recent weeks.
He mentioned Hungary's great dependency on Russian energy supplies arriving through Ukraine and said that the 200,000 ethnic Hungarians living in western Ukraine, near the border with Hungary, are also a factor shaping Hungary's policy.
During her visit to Budapest, Merkel was also expected to meet with representatives of German companies operating in Hungary, visit the Dohany Street Synagogue and a nearby Holocaust memorial, and speak at the German-language Andrassy University.