Formal, literary term used in written language or official contexts to refer to the current moment or present situation. Often appears in set phrases like 刻下の情勢 (the current situation).
刻下の情勢を踏まえて、対策を講じる必要がある。
We need to take measures based on the current situation.
刻下、我が国は未曾有の危機
At present, our nation is facing an unprecedented crisis.
Composed of 刻 (time, moment) and 下 (under, current). The combination literally suggests 'under the present moment', i.e., the current time. The exact historical derivation is uncertain, but it is a Sino-Japanese compound used in formal writing.