The potential motion at the SNP conference, to be held in October, calls to begin the process of "commissioning a specialist provision and recruiting staff to provide specialist services” for abortions up to the legal limit.
As it stands, no health board in Scotland provides abortion care up to the legal limit of 24 weeks.
In June, Scotland on Sunday revealed since 2019, 170 Scottish women have been sent across the border to England to have mid-trimester abortions.
The resolution states the specialist service, “would end the need for women, in this difficult position, to have to travel to England to receive services”.
The call is part of a raft of measures on abortion care submitted by Kat Cary, from the Edinburgh SNP branch, and Mhairi Love, from the Glasgow Provan SNP branch.
So far, the resolution has been signed by the entire SNP Edinburgh council group as well as members of Glasgow and Aberdeen branches, MP Gavin Newlands and MSP Rona Mackay.
It comes as Scotland has seen a recent rise in anti-abortion protests across the country with more from the group 40 Days for Life expected to take place in September.
The Scottish Government has confirmed a second abortion summit will take place at the end of August to discuss action to protect women accessing services at a local authority level.
At the last summit, the First Minister said the Scottish Government was considering test councils, specifically Edinburgh and Glasgow, to implement 150m anti-abortion protest buffer zones.
The resolution calls on the Scottish Government to ensure national buffer zone legislation is enacted.
It also calls for assurances that home abortion services implemented during the pandemic are a permanently available service.
Nicola Sturgeon previously said she is ready to “dig into” legislation around 150m protest prevention buffer zones called on by campaign group Back Off Scotland.
The Scottish Government is investigating whether to back a private members’ bill by Green MSP Gillian Mackay, to introduce the zones at national level.
Ministers are waiting for the UK Supreme Court to rule on a Northern Irish case around exclusion zones before determining the legislation for Scotland.
There will be a third Scottish Government abortion summit in roughly six months to discuss “broader” issues, including national legislation of buffer zones.
The submitted motion calls upon the Scottish Parliament to establish an expert review of existing legislation, adding: “Conference respects the principle of free speech regarding abortion rights. Conference also recognises that the right to free speech is not absolute and that legal limits should be placed on speech that contravenes the rights of others, which causes harassment, alarm, and distress.”
Lucy Grieve, co-founder of Back Off Scotland, said: “We’re grateful to Kat Cary of the Edinburgh SNP branch and Mhairi Love of the Glasgow Provan SNP branch for submitting this resolution and for their work in drumming up support locally and nationally, with the recently appointed COSLA President throwing her support behind this.
"We therefore call on the conference committee to commit to putting this on the official conference agenda.”