Does "pressing for stakes" mean "urgently needing the share/benefits"?

Used this way, it means the Kremlin is pressing for a percentage of ownership. Possibly, the phrase could be stretched to mean influence instead of ownership.

Pressing can mean urgently but in this case it means pressure. The suspicion is that Russia is putting pressure on something to gain stakes, shares, a piece of the action, in the some gas fields somewhere and this is somehow putting pressure on Cyprus, one would imagine.

Yeah, they've found natural gas fields in offshore Cypriot territory and Russia wants in on the action in exchange for financial aid for Cyprus' economic crisis.

http://www.guardian.co.uk/world/2013/mar/20/cyprus-keeps-banks-closed-talks-continue

"getting a stake" in a business or venture is getting part of the action.

The Kremlin is aggressively making the moves (loans, aid, etc) to get a part of the action . .

Thanks, I did read about it later. Terrible situation, really.