The comments from Gabriel, economy minister as well as Chancellor Angela Merkel's deputy, came during a trip to Tehran aimed at rebuilding badly affected trade ties.
Gabriel, the most senior Western official to visit since last week's nuclear agreement between Iran and six world powers including Germany, said the deal had laid a foundation for better cooperation but differences remained.
"With the nuclear agreement and the economic recovery that will surely come after it, Iran will also bear new responsibilities, at home and abroad," he told delegates at a conference in the capital.
"You must understand that for us Germans, the security of the state of Israel is also of great importance.
"I understand how difficult the debate is, and we in Germany also believe that the Palestinians have a right to their own state. That must be our shared international goal."
Iran does not recognize Israel as a state and officials routinely refer to its leaders as "the Zionist regime".
On July 10th, as negotiators from Iran and the P5+1 powers sought to conclude the nuclear deal, tens of thousands of people gathered in Tehran for annual Quds (Jerusalem) Day demonstrations in support of the Palestinians.
As is customary at such gatherings the crowd chanted "Down with Israel" and carried placards that declared "Zionist soldiers kill Muslims". They also burned Israeli and US flags.
However, Gabriel said differences over Israel should not affect efforts to improve Iran-German relations after the nuclear deal, which has given hope to a major economic revival in the Islamic republic when sanctions are lifted in coming months.
"The test of true friendship is when you can discuss difficult issues openly, in a spirit of partnership and respectfully -- that shows how close the friendship is," Gabriel said.
"Nothing needs to change in that friendship, even if we hold different views."
Iran's foreign ministry spokeswoman Marzieh Afkham also sought to isolate the disagreement about Israel, saying such differences were not new and had not affected other "constructive contacts".
"We have completely different positions on regional issues with Germany, and over the last 35 years we have expressed on many occasions, in negotiations, our positions very clearly," she said, according to the ISNA news agency.
"The main part of the dialogue is about the prospect of bilateral cooperation and naturally we will express our concerns about the region, including existing threats, including threats of the Zionist regime and the
roots of the crises in the region."