EU to invite Iran FM Zarif for talks over protests: Berlin
"Together with the EU's foreign policy chief (Federica Mogherini), we agreed to invite the Iranian foreign minister, if possible next week," Gabriel told German public broadcaster ZDF, without giving further details.
Hundreds more protesters were arrested since 28 December demonstrations against inflation and Iran's sluggish economy, which eventually turned against the Iranian regime as a whole.
Attacks were reported on government buildings and police stations, while human rights groups condemned the use of "excessive force" by Tehran.
Iran's elite Republican Guards are believed to have played a role in quashing the unrest.
"We very quickly affirmed that we support the freedom to demonstrate and that the state should support this," Gabriel said.
At the same time, Gabriel said Berlin will not follow the lead of US President Donald Trump, who pledged to help Iranians "take back" their government.
Trump also seized on the recent unrest to again slam a multiparty nuclear deal with Iran as deeply flawed.
Germany, as well as France, has "warned against attempts at instrumentalising the domestic conflicts in Iran," said Gabriel.
The US on Friday took the Iran protests to the UN Security Council, where deep divisions emerged over the issue, with Russia arguing the demonstrations posed no threat to international peace and security.