To pursue a claim for malicious falsehood, you must show that the statement was both false and was made maliciously, meaning that the other party either knew that it was untrue, or were reckless to the fact. Their liability may be mitigated considerably if they quickly publish a corrective statement acknowledging the falsehood because this will diminish the element of malice.
In most cases, you will also need to show that loss or damage has been suffered as a result.