The German minister, who arrived in the region on Saturday and held talks with top Israeli and Palestinian officials, called for efforts to rebuild the shattered enclave which was ravaged by a 50-day war last summer, the third in six years.
But he said it would only be possible if there was a halt to Palestinian rocket fire on southern Israel.
"I came out of all my discussions yesterday in Jerusalem and in Ramallah with the hope that all parties are mindful that here we are sitting on a powder keg here and that we must ensure that the fuse does not catch light," Steinmeier said.
"We shall only be able to decisively reduce the risks of a fresh escalation if we allow economic development in the Gaza Strip in addition to humanitarian aid and reconstruction," he said on a visit to Gaza City's fishing port.
That would only be possible "with open borders" -- a reference to the tough restrictions on the movement of goods and people that have been imposed by Israel and Egypt.
"But none of this will succeed until it is certain that there will be no further rocket attacks from here, when it is no longer a launch pad," he said.
During his visit, Steinmeier toured a German-funded girls school in the beachfront Shati refugee camp in Gaza City.
But he did not meet any officials from Hamas, the de facto power in Gaza that is designated by the European Union as a "terrorist organisation".
Last year's deadly conflict claimed the lives of more than 2,200 Palestinians, most of them civilians, and 73 people on the Israeli side, most of them soldiers.
A World Bank report published in May said Gaza's unemployment rate of 44 percent was "probably the highest in the world" which, coupled with its soaring poverty levels, was "very troubling".