The amendments, which would have stopped any land ownership in Scotland by companies and trusts not based in the EU, were brought by Patrick Harvie MSP.
The Scottish Government has been resistant to the idea, despite recommendations from the Committee in its stage one report, the Land Reform Review Group and clear support in public consultation.
The Scottish Greens have consistently called for bold action to make land ownership clearer and fairer and are currently running an online petition so that the public can back the party's bid to amend the Bill to include vacant land so it can be taxed with funds used for housebuilding.
The amendment on vacant land is expected before the Rural Affairs Committee in the coming weeks.
Andy Wightman, Land Reform spokesperson for the Scottish Greens and MSP candidate for Lothian, said:
"The committee's refusal to include an EU registration clause in the Bill is extremely disappointing and the continued resistance of Ministers shows how timid the Scottish Government are on this issue.
“By stopping ownership based in tax havens we could have taken advantage of the EU's drive to tackle laundering and secrecy. I hope we have greater success with our amendment on vacant land. Scotland can bring land ownership into the 21st century but we need Holyrood to be bold.”