The EU and US have announced travel bans and asset freezes against a number of officials from Russia and Ukraine.
The moves follow Sunday’s referendum in Crimea, in which officials say 97% of voters backed breaking away from Ukraine and joining Russia.
The individuals targeted by the sanctions are seen as having played a key role in the referendum, which Kiev, the US and EU deem illegal.
Pro-Russian forces have been in control of Crimea since late February.
Moscow says the troops are pro-Russian self-defence forces and not under its direct control.
The crisis follows the ousting on 22 February of Ukraine’s pro-Moscow president Viktor Yanukovych, who had sparked months of street protests by rejecting a planned EU trade deal in favour of closer ties with Moscow.
US President Barack Obama said in a press conference that Washington stood “ready to impose further sanctions” depending on whether Russia escalated or de-escalated the situation in Ukraine.
If Moscow continued to intervene in Ukraine, he warned, it would “achieve nothing except to further isolate Russia and diminish its place in the world”.