It is the latest blow for a government determined that a February election will go ahead despite deadly clashes with protesters.
General Prayuth Chan-ocha said "the door was neither open nor closed" when asked whether a coup would happen: a marked shift from the strong denials the armed forces routinely make.
He added: "Anything can happen. It depends on the situation. We are trying to do the right thing, in a peaceful way and we urge negotiations."
The general's comments represent a major setback at a critical time for Prime Minister Yingluck Shinawatra, who is under attack from opponents determined to overthrow her and weaken the influence of her self-exiled brother, former premier Thaksin Shinawatra.
She has called an election for February, which her Puea Thai Party is almost certain to win, but anti-government protesters have vowed to stop the poll.
The Election Commission (EC) also asked for a postponement after violent clashes on Thursday.
The political deadlock and violence have become all too familiar in Thailand, where the military have staged or attempted to stage 18 coups in 81 years of democracy.
South-east Asia's second-biggest economy is divided broadly between those who love Thaksin, such as the rural poor in the populous north and north-east, and those who loathe him, a group that includes Bangkok's conservative elite and middle class.
The events of the past few days suggest powerful forces could again be at work to undermine Thaksin's populist political machine, which has won every election since 2001.