Trump said Washington was weighing if the deal serves its security interests, but Germany and other powers fear its collapse could trigger regional arms race.
German Foreign Minister Sigmar Gabriel said any US move to abandon the Iranian nuclear deal would discourage other powers such as North Korea from negotiating an end to their own atomic programmes.
Gabriel, speaking on the sidelines of a UN meeting in New York, said much work would be needed in coming weeks to preserve the 2015 agreement – under which Iran curbed its nuclear work in exchange for the lifting of sanctions.
The United States said on Wednesday it was weighing whether the nuclear deal serves its security interests.
"It's an almost tragic situation where the only existing agreement to prevent the proliferation of nuclear weapons is in jeopardy at a time when we are seeing other countries like North Korea acquiring nuclear weapons and we need such processes more than ever," Gabriel said.
In Berlin, German Economy Minister Brigitte Zypries said Germany, as one of Iran's most important trading partners in Europe, had a "great interest" in preserving the agreement that had opened up Tehran economically.
"We want to continue to fill this agreement with life," Zypries told Reuters. German exports to Iran rose 23 percent to $1.7 billion (1.4 billion euros) in the first half of 2017.
US President Donald Trump has called the Iran deal "an embarrassment," but Germany and other powers who also negotiated it with Iran fear a collapse of the agreement could trigger a regional arms race and worsen Middle East tensions.
Gabriel said Trump had received no support for his position from other world powers.
The foreign minister said he accepted the US position that Iran's behaviour in the Middle East had not improved since the deal – but said there was no hope of it changing its ways if the accord fell.
Any collapse would send a "terrible signal" for other diplomatic efforts "because no one has the impression anymore that international negotiations are worthwhile and one has to assume that such an agreement can be cancelled after a short time," he said.
Trump must decide by October 15 whether to certify that Iran is complying with the pact. If he does not, Congress has 60 days to decide whether to reimpose sanctions waived under the accord.
Iran said on Wednesday it did not expect Washington to abandon the agreement.