Chancellor Merkel defended her decision to open German borders in 2015, while also urging European Union countries to show solidarity on refugees.
Over a million refugees and asylum seekers crossed into Germany in 2015 and a lot of them stayed in the country.
"We demand the release of Deniz Yücel, Peter Steudtner and Mesale Tolu", Merkel said in reference to three German citizens (a journalist, a human rights activist and a translator, respectively) imprisoned in Turkey.
Merkel's remarks, less than a month before the German election, suggest she has little appetite for the kind of sweeping overhaul of the eurozone that countries such as France have been advocating.
"There are many issues where people have the feeling that Merkel is out of touch", Schulz said in an interview on public broadcaster ARD.
Even though Merkel's conservative Christian Democrats are far ahead of the center-left Social Democrats (SPD) in opinion polls, some conservative voters are angry that she has opened Germany's borders to more than a million refugees since late 2015.
"The head of government has to act and I did", she added".
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She said the policy was justified in that year because of the emergency situation during that particular period.
Her response to the migrant crisis has inflicted political damage on her party with the right-wing Alternative for Germany (AfD) party expected to win 10% of the vote in September.
"Either we [in Europe] show solidarity with countries like Italy and Greece or this will have grave impact in the future", she said.
The checks were first introduced in response to the worst refugee crisis since World War II, which saw a record number of refugees flood into Europe from Syria, as well as other Middle Eastern countries and Africa.
Merkel on Saturday encountered fierce protest in an election campaign rally in Quedlinburg in eastern Germany's state of Saxony-Anhalt, where the anti-foreigner sentiment is obviously strong.
"I'm happy to say those two words out loud", she said.
At least one reporter wanted to know why Merkel only appeared once a year for a major press conference on her own, accusing the chancellor of being more media shy than President Donald Trump or Russian President Vladimir Putin.