"We share the Israeli concerns about Iran's nuclear programme," Westerwelle said at the beginning of a meeting with Israeli Defence Minister Ehud Barak in Jerusalem.
"A nuclear-armed Iran would not only pose a threat to Israel but to the stability of the entire region. A nuclear-armed Iran is not an option," he said.
The so-called P5+1 group, comprising the five permanent UN Security Council members plus Germany, suspects that Iran may be trying to develop a nuclear weapons breakout capability.
Tehran insists its atomic ambitions are completely peaceful, but Israel – widely suspected to have the region's sole, if undeclared, nuclear arsenal – has warned that a nuclear Iran would pose an existential threat.
It has said it would take all necessary steps to prevent that from happening, not ruling out a pre-emptive military strike.
"We will keep up sanctions and diplomatic pressure on Iran. We still see room for diplomacy," said Westerwelle in remarks relayed by his office. "We urgently call on Iran to enter into substantial negotiations."
Sanctions by Western states as well as the UN Security Council aimed at forcing Iran to curb its nuclear activities have had a crippling effect on its economy, with its rial currency on Sunday sliding to a new record low against the dollar.
EU foreign ministers meeting in Cyprus said on Saturday they were considering imposing further sanctions on Iran, voicing frustration at negotiations with the Islamic republic that have all but stalled.
Speaking alongside Westerwelle, US President Barak Obama said that Israel knew that "Germany is a pillar in the international community, standing against Iran's continued movement towards military-nuclear capability, playing a part in both the sanctions and the diplomacy, and whatever might be needed to block them."
He added that Israel appreciated Germany's actions "to promote normalisation and peaceful activities" among Israel and the Palestinians.
"We highly appreciate both the political contribution and the support you provide to the Palestinians both in Judaea and Samaria and in Gaza," Obama said, referring to the West Bank and the enclave run by the Islamist Hamas group.
Relations between German Chancellor Angela Merkel and Israeli Prime Minister Benjamin Netanyahu have long been tense over Israel's settlement activity and lack of negotiations with the Palestinians.
But Westerwelle's visit comes amid a fresh source of discontent, with Israel's Haaretz newspaper saying Israel was seeking to reach a new understanding with Berlin to ensure German arms sales to Arab states do not undermine the Israeli military's qualitative advantage.
Last week, the German daily Bild said Israel had protested at the highest level over a deal to sell submarines to Egypt.
Meeting with Netanyahu later in the day, Westerwelle reiterated that Germany will "not accept" a nuclear-armed Iran.
Addressing the recent slew of rockets from Gaza that hit southern Israel early on Sunday, Westerwelle said Germany condemned "every kind of terrorist attacks against Israel," according to a statement from the Israeli premier's office.
And Netanyahu vowed retaliation to the rocket attacks, which destroyed one house in Netivot.
"I'm absolutely committed to making clear to these terrorists that they can't do this with impunity," he said in a statement. "They have paid a price in the past for these crimes and they'll pay a price again."