Ministers are set to meet on Monday to discuss Syria amid the prospect of Western military action in response to the suspected use of chemical weapons.
During a press briefing on Friday, Mr Lavrov said he had "irrefutable evidence" that the attack was staged as part of a "Russophobic campaign" led by one country, which he did not name.
White Helmets first-responders and Syrian activists have claimed the suspected chemical attack was carried out by the Syrian government on April 7 and killed more than 40 people in Douma, allegations that drew worldwide outrage and prompted the USA and its allies to consider a military response.
Following the joint attack in Damascus against the Assad regime, Russia's ambassador warned that there will be consequences for the US-led military strikes on Syria, adding that it was unacceptable to insult Russian President Vladimir Putin.
"We have information indicating Russian intelligence service interest in the Skripals, dating back at least as far as 2013, when email accounts belonging to Yulia Skripal were targeted by GRU cyber specialists", he said, referring to Russia's foreign military intelligence agency.
Speaking to reporters in Moscow, Lavrov reiterated a strong warning to the West against military action in Syria.
Antov added that it was not acceptable to insult Russia's president: "Insulting the President of Russian Federation is unacceptable and inadmissible".
Zakharova suggested that Western media bore some responsibility for the strikes, claiming the White House cited "multiple media sources" on the suspected chemical weapons attack in Douma.
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In the United Kingdom, cabinet ministers agreed that it was "highly likely" the Assad regime was responsible for the alleged attack and said the use of chemical weapons must not "go unchallenged".
A fact-finding mission from the Organization for the Prohibition of Chemical Weapons is expected to head to Douma, the site of the suspected attack.
The council failed on Tuesday to approve three draft resolutions on chemical weapons attacks in Syria.
But Nebenzia said the goal was to oust President Bashar al-Assad from power.
Russian Federation has been deeply enmeshed in Syria's civil war since 2015 and Washington and Moscow have already indirectly clashed in the country. Both the Syrian and Russian governments have said they would support the study.
Another senior official said Trump and his aides had largely settled on a consensus view on what strategy to take and that work continued on the timing and coordination with allies who plan to participate. The government's capture of Douma, the last town held by the rebels in eastern Ghouta, marked a major victory for Assad.
'We can not allow the use of chemical weapons to become normalised - within Syria, on the streets of the United Kingdom, or anywhere else in our world.