Brexit Secretary Mike Russell says the decision has been taken after the UK Government moved to "retrospectively limit" Holyrood's power, without consent.
But new laws will be brought forward to allow Holyrood to "keep pace" with the EU after Brexit, it was confirmed today.
The Scottish Government brought forward it's own UK Continuity Bill amid concerns that the UK Government's own Withdrawal Act was an attack on the powers of the Scottish Parliament over the way responsibilities returning from Brussels were to be repatriated.
Holyrood's Presiding Officer Ken Macintosh ruled it was outwith the powers of the Scottish Parliament. However, the Uk Supreme Court found the Bill had been competent when first lodged - but UK ministers retrospectively moved to Alter the Scotland Act and render the Bill incompetent.
Mr Russell said today the Supreme Court ruling had "profound implications" for devolution.
"The Court held that when the Scottish Parliament passed the Continuity Bill it had the power to decide what should be done, in devolved Scots law, to protect our system of laws from the damaging consequences of EU exit," he said in a letter to Holyrood's Presiding Officer Ken Macintosh.
"That power was circumscribed by a later Act of the UK Parliament. In other words, the Scottish Parliament had the power to make different choices, such as the decision to retain the Charter of Fundamental Rights where the UK Government decided not to, but that power was removed by the UK Government’s EU (Withdrawal) Act, an Act passed without the consent of the Scottish Parliament.
Mr Russell added: "That being the case - the Continuity Bill having been in part retrospectively denuded of its force - Scottish Ministers have reluctantly come to the conclusion that we should not at this point move for its reconsideration."
"This decision has been taken following a series of meetings with representatives of parties across the Chamber."
Scotland will continue to develop its own policy for future environmental principles and governance, Mr Russell adds.
"We shall put in place the legislative and institutional arrangements that will be required," he adds.
Ministers are also looking at the ways to protect teh welfare needs of animals, he added.
And work to respect the commitment to retaining the Charter of Fundamental Rights in the Continuity Bill will also be taken forward thorugh a National Task Force.
And new laws will be passed to keep Scotland attuned with EU law.
"The extent to which devolved law aligns itself with the law of the EU should be a decision for the Scottish Parliament to take, not the UK Government," Mr Russell added.
"This Government is committed to no regression in standards or protections should EU exit take place, and the replacement of regulatory powers lost in consequence of EU exit will be essential to ensure that."