SNP MP have backed a push for control of abortion to be handed to Holyrood - despite concerns from women's and human rights groups that the move would lead to cross-border travel for terminations.

Campaigners had also warned that transferring the power from Westminster could lead to tougher laws north of the border.

The Scottish Government quietly dropped a demand for new powers over abortion earlier this year, saying that it was concentrating on other priorities instead.

But a move to devolve the powers to the Scottish Parliament was tabled to the Scotland Bill by three pro-life MPs from other parties.

An SNP source said that the party did not want to change the current law on abortion.

But, he added: "We're in the more powers business."

Abortion was one of the most divisive issues during the Smith Commission negotiations on further powers for Scotland, in the wake of the independence referendum.

The cross-party talks almost collapsed after abortion became a 'red line' for Labour.

The row erupted amid fears of potentially different legal limits on termination on either side of the border.

Campaigners warn that this could lead to a cross-border traffic in abortions.

At the weekend 17 individuals from organisations including Amnesty International, the Human Rights Consortium Scotland and Scottish Women's Aid signed a statement to MPs raising fears that devolution could lead to different laws north of the border.

It read: "We are already in the situation in the UK where different legal frameworks on abortion have resulted in a discriminatory impact against women and girls in Northern Ireland, for which the UK has been repeatedly criticised internationally.

"Our concern is that this strategy of hasty devolution is being used in order to argue for regressive measures and in turn, a differential and discriminatory impact on women and girls in Scotland.

"Women across the UK have fought for women's bodies to be their own, and to this day, fight opposition to a women's right to choose.

We do not wish this amendment to open the doors to those who seek to undermine this right."

In the end the Smith agreement said that "further serious consideration should be given to its devolution and a process should be established immediately to consider the matter further".

But earlier this year the Scottish Government signalled it had given up on its demand.

An SNP source made clear that the issue was no longer a priority for the party.

The SNP spokesman said last night: "As the Smith Commission reported, the parties were 'strongly of the view' that responsibility for abortion should be devolved, given that health as a whole is devolved."

SNP MP Stewart McDonald told MPs that he backed the devolution of abortion and he found it "offensive" that some had characterised the debate as a choice between nationalism and feminism.

Shadow Scottish Secretary Ian Murray said that a woman's "right to choose should be based on medical evidence and not by where they live."

He said Labour agreed with the 13 organisations from Scotland which had raised fears about the consequences of devolving abortion.

He added: "We have a shared concern that this has not been properly consulted on and will harm women's right to choose."

The clause that would have transferred powers to Holyrood was proposed by three MPs in the All-Party Parliamentary Pro-Life Group, including one Conservative, one Liberal Democrat and one Labour MP.

The expectation was that it would be defeated, but ultimately it was not put to a vote.