In a phone call with his US counterpart John Kerry, Mr Lavrov said imposing sanctions on Moscow would harm the US.
Pro-Russian troops have been in control of Crimea for the last week.
Earlier, a stand-off involving pro-Russian soldiers at a Ukrainian military base outside Sevastopol reportedly ended without incident.
Crimea's parliament announced on Thursday it would hold a referendum on 16 March on whether to join Russia or remain part of Ukraine.
Russia's parliament has promised to support Crimea if it chooses to become part of Russia.
The vote has been denounced as "illegitimate" by the interim government in Kiev, which took power after President Viktor Yanukovych fled to Russia last month in the wake of mass protests against his government and deadly clashes with security forces.
In their telephone conversation on Friday, Mr Lavrov warned Mr Kerry against taking "hasty and unthought-through steps capable of causing harm to Russian-US relations", Russia's foreign ministry reports. (+ BBC video) » | Saturday, March 08, 2014
