Most Helpful Girl
It could mean that she wants one but be wary. You were together for a long time and she could just miss the comfort of the relationship and not actually being in one with you. During the first few months after a break up, especially if the relationship was so long term, we tend to focus on the good times of the relationship and can begin to romanticize it. It can lead us to wanting a reconciliation only to make us quickly change our minds once we get involved again. It creates a vicious cycle and one person often gets hurt over and over again in the process.
Give it time. Talk with her when she's feeling less emotional. Have a rational discussion and set boundaries to find out if this is what she really wants. Tell her that if she wants to work it out it's the last chance and this time it's all or nothing. Before you jump in to it have a long discussion about why things ended, and how you both contributed to the decline in the relationship. Make decisions together how to go about working on your issues and determine if things are in fact workable or not. Being hasty about this isn't going to solve anything.
Most Helpful Guy
Who left who? Can the reason for the split be put right? Has she been with another guy, in that month, that turned out to be abusive? If she's been with another guy, would you take her back?
Just a few questions to ask yourself.
In answer to your question, yes, I think it's highly likely she does want reconciliation. Nobody can tell you what to do. You must make a decision yourself. Tread carefully, so you don't get hurt (again?). Find out from her what she wants. You don't have anything to lose by finding out. You have the final say if you feel able to make it up.