I would leave him. I spent my 30's with a guy who kept saying he loved me but we would try in 6 months time... He would always come up with excuses. Then he said he didn't want kids at all...
That man took my most fertile years. I was loyal so for a good few years I tried to explain his reasons and be okay with it.
It became unbearable so I left him.
From my experience (my own dating history and that of many friends in London) if a man doesn't want commitment or doesn't want kids it's cos he's not that into you. Values are what make a successful relationship and if they don't match on a fundamental thing about family then it's a red light warning sign.
Then, at 39 met my now-husband.
My amazing husband is the love of my life, doesn't care at all that I'm older than him and can't wait to have kids. We're positive but the problem is that I'm 43 now and we've had miscarriages but no kids yet. Experts reckon you have until 45 and believe me in our situation time goes by so fast.
So.... You can assume you have time and try for babies later in life, and many women do so with a happy ending...but there's no guarantee. If having a successful pregnancy is not straight forward (and you won't know til you try, my eggs are healthy and all tests amazing for my age but I miscarry and it's harder to know why) then you have less time to play with. There's more help than ever before, but IVF isn't available at my age and chance of success is 9-15% per cycle.
My husband loves me no matter what and the path of my life led me to him, so I can't and don't regret it now. I just would hate to see other lovely women let a man take their chance of motherhood away.
(As an addendum, my ex eventually came crawling back again and again begging me to take him back, saying I could have a baby... All despite my being very firm and clear that there was absolutely no chance and asking him not to contact me. He's still single after a string of disasters).