"We can't just accept this without responding", Maas said.
Britain and its allies are bracing for possible retaliatory attacks in the region by Iran and its proxies in revenge for the assassination of Major General Qasem Soleimani as he was being driven out of Baghdad airport last week.
In that context, Pompeo said that if the USA military were to strike inside Iran, in the event Iran retaliated against America for the Soleimani killing, those strikes would be legal under the laws of armed conflict.
The US president defended his threat and said if the Iranians were allowed to "torture and maim our people. use roadside bombs and blow up our people" then the US could target cultural sites.
"France fully shares with Germany the central objective of de-escalation and preservation of the Vienna (nuclear) accord", Foreign Minister Jean-Yves Le Drian said.
"There are global conventions in place which prevent the destruction of cultural heritage", he said.
Iran's latest announcement came after a USA drone strike Friday killed the commander of the Revolutionary Guards' foreign operations, Qasem Soleimani, in Iraq. "It is in everyone's interests that the deal remains in place", Mr Johnson's spokesman said.
Iran's state television later reported that the country will no longer abide by any of the limits of its 2015 nuclear deal.
Iran will continue its cooperation with United Nations nuclear watchdog.
Earlier on Sunday, the Ministry of Foreign Affairs confirmed that the head of business of the German embassy in Tehran had met with officials of the Ministry of Foreign Affairs of Iran, but did not provide details.
Zarif wrote: "Targeting cultural sites is a WAR CRIME".
"Clearly our first priority is to make sure that United Kingdom nationals, citizens, shipping, diplomatic missions and military personnel are safe".
Germany's foreign minister said Sunday that he has proposed bringing forward a regular meeting with counterparts from other European Union countries to the coming week amid escalating tensions in the Middle East.
Trump tweeted afterwards that his administration had already "targeted 52 Iranian sites (representing the 52 American hostages taken by Iran many years ago), some at a very high level & important to Iran & the Iranian culture".
Meanwhile, Donald Trump spoke with UK Prime Minister Boris Johnson on Sunday, discussing the current situation in Iraq and Iran, the White House said in a statement.
Iran's Supreme National Security Council Secretary Ali Shamkhani told state television the Iraqi parliament's vote means the US military presence in Iraq is considered an occupation.