Lavrov made the comments on March 13, after the United States said it was ready to act in Syria to end chemical attacks and 'inhuman suffering' if Russia, Iran, and Syria continue to allegedly ignore the truce approved two weeks ago.
'The UN Security Council did not promise the terrorists a break; what is more, it told them there would be no break,' Lavrov told a news conference in Moscow.
'Those operating on the ground in eastern Ghouta and led by the Al-Nusra Front do not want to meet their obligations,' he added. 'All they want is for the [Syrian] government to cease fire and give them a break.'
Late on March 12, U.S. Ambassador to the UN Nikki Haley told the Security Council that the cease-fire had 'failed' and the United States was offering a new 30-day truce, which she said has 'no counterterrorism loopholes' and will be harder for Syrian President Bashar al-Assad and others to ignore.
Haley accused Syria and its allies Russia and Iran of exploiting such 'loopholes' to 'continue starving and pummeling hundreds of thousands of innocent Syrian civilians' in Ghouta, the last opposition-controlled pocket near Damascus.
UN Secretary-General Antonio Guterres told the council that air strikes, shelling, and ground offensives had only intensified in eastern Ghouta since the UN declared a 30-day cease-fire on February 24.
If the warring parties continue to ignore the truce, Haley said, the United States is prepared to take action on its own. She pointed to President Donald Trump's decision last April to order U.S. missile strikes on a Syrian air base that he said was used to launch a sarin gas attack that killed nearly 100 Syrian civilians.
Speaking in Moscow on March 13, the chief of the Russian armed forces general staff said that the Russian military would take 'retaliatory measures' targeting missiles and their delivery vehicles 'if a threat to the lives of our servicemen emerges.'
Without offering concrete evidence, General Valery Gerasimov also claimed that Syrian militants are planning to stage a 'provocation' involving the use of chemical weapons in order to justify what he said would be a subsequent U.S. strike on government-held neighborhoods in Damascus.
Rather than impose a full cessation of hostilities as called for by the UN, Russian officials say they have enforced five-hour daily breaks in the fighting that they say have allowed the evacuation of civilians and the injured from battle areas while allowing the delivery of some humanitarian aid.
On March 13, Syrian state television showed a group of sick and injured civilians leaving eastern Ghouta for government territory.
Meanwhile, the Russian military said that around 100 people had left the town of Duma in the Ghouta area.
Yasser Delwan, a member of the largest rebel group in the besieged region, confirmed that a group of patients had left under a deal for a medical evacuation with the Syrian government's key ally Russia.
However, the group Jaysh al-Islam vowed not to leave the area and to continue fighting advancing Syrian government forces.
At least 1,162 civilians have been killed, including 241 children, in the nearly month-long Syrian offensive to retake eastern Ghouta from armed rebels, according to the Syrian Observatory for Human Rights.
Russia, along with Iran, has given Assad's government crucial support throughout the seven-year war in Syria, which began in 2011 with a government crackdown on peaceful protests.
Moscow helped turn the tide of the conflict in Assad's favor by launching a campaign of air strikes in 2015 and stepping up its military presence on the ground.
With reporting by AFP, dpa, Reuters, AP, TASS, and Interfax