His comments stepped up Moscow's war of words with the United States and the European Union in their worst diplomatic standoff since the Cold War ended.
"As for the concept behind the use of coercive measures, the West is making clear it does not want to force Russia to change policy but wants to secure regime change," Tass news agency quoted Lavrov as telling a meeting of the advisory Foreign and Defense Policy Council in Moscow.
He said that when international sanctions had been used against other countries such as Iran and North Korea, they had been designed not to harm the national economy.
"Now public figures in Western countries say there is a need to impose sanctions that will destroy the economy and cause public protests," Lavrov said.
His comments followed remarks in which President Vladimir Putin said Moscow must guard against a "color revolution" in Russia, referring to protests that toppled leaders in other former Soviet republics, Reuters reported.
Western sanctions have limited access to foreign capital for some of Russia's largest companies and banks, hit the defense and energy industries, and imposed asset freezes and travel bans on some of Putin's allies.
The measures have aggravated an economic downturn, which has also been worsened by a fall in global oil prices and has helped cause a nearly 30 percent slide in the rouble against the dollar since the start of the year.
Putin's popularity has soared in Russia since the annexation of Crimea from Ukraine in March.