Nicola Sturgeon has put her independence referendum plans temporarily on hold after announcing a "reset" of her proposed timetable.
The first minister had called for an independence referendum to be held in the autumn of 2018 or spring of 2019.
But Ms Sturgeon told Holyrood she would now delay her plans to introduce legislation for a referendum.
However, she later said it was still "likely" a referendum would be held by 2021.
Ms Sturgeon has been considering her options since the SNP lost 21 seats in the election earlier this month.
She said the Scottish government would delay its proposed referendum legislation until at least the autumn of next year - although it would still need the permission of the UK government for a legally binding vote to be held.
In the meantime, she said she would "redouble" her efforts to secure the best possible Brexit deal for Scotland, and to keep the country in the European single market.
Ms Sturgeon stressed that she continued to be "strongly committed" to Scotland having a choice on its future at the end of the Brexit process.
And the first minister later told journalists she believed it was still "likely" there will be a second referendum on independence during the lifetime of the current Scottish Parliament, which is due to last until 2021.
UK Prime Minister Theresa May had earlier urged Ms Sturgeon to take the possibility of a second referendum off the table completely.
And Unionist opposition parties in the Scottish Parliament claimed Ms Sturgeon had not gone far enough, and that "nothing has changed".
The pro-independence Scottish Greens urged the SNP leader not to retreat on her referendum bid, and to "continue fighting" for another vote on the issue.
Ms Sturgeon has previously said that the prospect of an independence referendum was a factor in the election result, which saw her party's share of the vote drop from 50% to 37%.
However, the SNP remained by far the largest party in Scotland after winning 35 of the country's 59 seats at Westminster.
Backtrack not U-turn
Analysis by Sarah Smith, Scotland editor
Anyone waiting to declare that Nicola Sturgeon has been forced to do a U-turn over her plans for a second independence referendum will have been sorely disappointed today.
She has been forced to backtrack on the timing. The first minister is no longer insisting that any independence vote takes place before the UK leaves in EU in March 2019.
But she has told the BBC that there could still be another referendum before the end of this Scottish Parliamentary term in 2021.
In the parliamentary chamber this afternoon she said had listened to voters and reflected on the result.
Ms Sturgeon said she had repeatedly been told during "hundreds" of conversations since the election that people were worried about the uncertainty caused by Brexit, and wanted a break from making big political decisions.
The first minister said people also wanted greater clarity about the implications of Brexit to emerge, and that it was "too soon right now" to make a decision about a referendum.
And she said people wanted the Scottish government to "focus as hard as we can on securing the best possible outcome for Scotland".Ms Sturgeon argued that the general election and the "weakness" of the UK government had "reopened the possibility, however narrow, of averting a hard Brexit and maintaining membership of the single market".
She added: "I want to reassure people that our proposal is not for a referendum now, or before there is sufficient clarity about the options.
"But rather to give them a choice at the end of the Brexit process, when that clarity has emerged.
"I am therefore confirming today that having listened and reflected, the Scottish government will reset the plan I set out on 13 March.
"We will not seek to introduce the legislation for an independence referendum immediately. Instead we will, in good faith, redouble our efforts and put our shoulders to the wheel in seeking to influence the Brexit talks in a way that protects Scotland's interests."
A plan not abandoned, but resting
Analysis by Brian Taylor, BBC Scotland political editor
Nicola Sturgeon intends to focus upon securing the best possible deal from Brexit for Scotland. She believes, further, that such a mission is made more feasible by a UK Government weakened by the absence of a single party majority.
So what has changed, in practice, as opposed to rhetorically?
- Firstly, Ms Sturgeon will not proceed now with legislation at Holyrood to prepare for a prospective referendum. The Bill will lie dormant. Not abandoned, but resting.
- Secondly, that means there is now no urgency about her demand for Westminster to transfer the necessary power to hold such a referendum, under Section 30 of the Scotland Act
Not, you understand, that the UK Government and the Conservative Party regarded the demand as urgent in the first place. The Scottish Secretary David Mundell has said not now, almost certainly not within the lifetime of the present Holyrood Parliament.
Ruth Davidson, the Scottish Tory leader, has come within a whisker of saying "not ever" - although, to be clear, she retains the option of indyref2 returning at some point.
So, one, the indyref2 Bill is shelved. Two, the Section 30 request is also on ice. But, three, the First Minister intends to return to the topic once Brexit negotiations conclude which she anticipates should be in Autumn 2018.
The Scottish government will also work to build "maximum support" across the UK for the proposals it set out at the end of 2016 - which argued for both the UK and Scotland to remain part of the European single market with "substantial new powers" for Holyrood.
She challenged the other parties at Holyrood to back her calls for Scottish government ministers to be "at the table" for Brexit negotiations.
And she added that when negotiations with the EU are complete and "when the terms of Brexit will be clearer", ministers would come back to the Scottish Parliament to "set out our judgment on the best way forward at that time".
'Impact of Brexit'
Ms Sturgeon said this statement, which is likely to happen next autumn, would also set out the Scottish government's view on "the precise timescale for offering people a choice over the country's future".
She said independence "may well be the only way to protect Scotland from the impact of Brexit" but insisted the case for independence "goes far beyond that".
"We must persuade the majority in Scotland of that. We have not done that yet but I have no doubt that we can," she added.
Scottish Conservative leader Ruth Davidson said Ms Sturgeon had failed to give people any assurance that she has been listening to them since the election.
Arguing that the first minister was "in denial" and "leaking credibility", the Tory leader added: "Her response hasn't been to reflect.
"It has been simply to lash out at the UK government at every opportunity and to sing the same old songs in the same old tune.
"She now claims to be putting the referendum to one side. She should just give the country some certainty and take it off the table for the rest of this parliament at least."
Scottish Labour leader Kezia Dugdale said: "The truth is the threat of an unwanted second independence referendum is dead and this didn't happen because Nicola Sturgeon wanted it to, the people of Scotland have taken that decision for her.
"The first minister is digging her heels in, putting her fingers in her ears and pressing on regardless. She is just not listening."
Scottish Liberal Democrat leader Willie Rennie said Ms Sturgeon's "long hard think" had led her to conclude that she should call another independence referendum at a time of her choosing.
He said: "The people spoke loud and clear at the general election that they did not want another divisive independence referendum. She should listen."