Foreign ministers from Britain, France and Germany - signatories of the 2015 deal to stop Iran developing nuclear weapons - held talks with Iranian Foreign Minister Mohammad Javad Zarif, amid concerns that the sanctions will also damage European business interests.
In a press conference with the visiting German counterpart, Lavrov slammed the U.S. pull-out as a "significant" violation.
European nations are moving to protect their companies from a resumption of stiff US sanctions on firms doing business in Iran, in a critical part of their bid to keep the Iranian nuclear deal alive and ensure it continues to benefit Iran's economy.
"We feel that the extraterritoriality of their sanction measures are unacceptable", he told the French daily Le Parisien.
Iran appeared determined not to be drawn into a wider regional conflict with Israel during the sensitive negotiations.
The EU's energy commissioner is also travelling this week to Iran to discuss strengthening European energy support to the Islamic Republic.
Iranian media reported that Foreign Minister Javad Zarif will visit the Chinese and Russian capitals on Saturday and Monday, respectively, before arriving in Brussels.
"It won't be easy, that's clear to all of us".
The steps forward underscored the EU's hopes that diplomacy and the promise of economic benefits might keep Iran in the fold of a nuclear deal that Europe sees as essential to security.
Since the lifting of sanctions, Russian Federation has signed a raft of agreements to play a role in Iran's energy and electricity sectors.
Earlier on Thursday, Russia's deputy foreign minister Mikhail Bogdanov called for "restraint on all sides", saying Russia was "concerned" at the escalation.
On Thursday, Israel claimed it had struck nearly all of Iran's military capabilities in Syria after the rocket attack on the Golan Heights, which Israel annexed in 1981.
France urged restraint, with French President Emmanuel Macron calling for a "de-escalation" in Syria.
Israel and its allies have blamed the Iranian Revolutionary Guards for initiating Thursday's exchange by launching missiles into the occupied Golan Heights.
"These attacks are a serious provocation that we strongly condemn".
In February 2016 then-US President Barack Obama signed the free trade agreement known as the TPP along with 11 other Pacific nations.
Russian Federation - which is alone in having close relations with both Iran and Israel - has sought to position itself as a mediator to prevent further escalation.
- The Seattle-Amazon tax fight is a lose-lose for everyone
- Ernesto Valverde ANGRY after seeing unbeaten record end
- Arsenal players 'shocked and upset' at surprise staff change
- C3, Diego Simeone dévoile la menace N°1 à l'OM — Atlético Madrid
- Boss Pep Guardiola: City will look to come back stronger next year
- Three reasons why Ireland were competitive in their inaugural Test against Pakistan
- Ranking the 5 best Eastern Conference teams LeBron James has destroyed
- Elon Musk restructures Tesla to iron out Model 3 production bottlenecks
- NBA Draft Lottery: What you need to know
- Harrison Ford digitally inserted into Solo: A Star Wars