I tried 'sentfrom' and 'sendtoaddress' api methods, but it looks like they ignore 'minconf=0' and return 'Insufficient funds' error.
Maybe 'createrawtransaction' will help me in my task?
As unamis76 has already mentioned, it can be done with the createrawtransaction, signrawtransaction, and send rawtransaction commands.
However, be aware that due to transaction malleability, it is possible that the transaction that you send could become invalid when the transaction that you receive becomes confirmed. In that case the third party address won't receive the bitcoins until you go back and rebuild a valid transaction.
Also be aware that it will be possible for the transaction that you receive to become invalid (intentionally or accidentally) before it confirms. If this happens, then the transaction that you send would also become invalid. You would need to contact whomever sent you the transaction in the first place to get them to re-send it, and then would need to re-send your own transaction.