Plans to let Holyrood decide the termination law were dropped from last week's Smith Commission on more powers at the last minute.
A leaked draft copy of the report shows abortion as being a power that should be devolved to Edinburgh but sources suggest Labour said the issue was a 'red line'.
SNP MSP Dave Thompson told Premier he thinks Labour vetoed the proposal.
He said: "It looks as if they have a real lack of confidence in Scottish MSPs and Scotland as a whole to deal with matters such as that which can as we know be difficult and delicate matters to deal with."
It's thought Labour were worried the SNP would lower the abortion time limit in a bid to please Christian backer Brian Souter.
Media reports claim Ed Miliband gave the go ahead for Labour's representatives at the devolution talks to walk out if abortion was not left out the agreement.
Premier has approached the Labour Party for a comment but is yet to hear back.