Merkel failed to criticize any of Orbán's authoritarian policies - putting large swathes of Hungary's mainstream media under state control and taking powers from the constitutional court.
Many commentators have pointed out that the policies echoed the conditions imposed under Hungary's old communist regime - whose political heirs, the Hungarian Socialist Workers' Party (MSZMP), Orbán outlawed.
A 2013 German TV documentary showed Orbán was breaking many of the European Union's own rules, raising suggestions that the bloc may be forced to impose sanctions on the country.
But on Thursday Merkel merely confined herself to saying that "the people's trust carried responsibility with it."
Orbán won 44.4 percent of the vote in the Hungarian election at the start of April, and is expected to be re-named government leader on Saturday.
The two leaders discussed the situation in Ukraine, which borders Hungary, and where around 200,000 Hungarians live.