Pete Wishart said the SNP could consider 'withdrawing from the apparatus of the UK state'.
In a letter to the UK Government, MSP Mike Russell said ministers had halted work on the plans as a result of the pandemic.
The country may also have to rejoin the Common Fisheries Policy, a report has said.
Angus MacNeil said if "all legal referendum avenues are blocked" then the party "must be able to use the ballot box" to win a mandate.
Labour leadership contender Lisa Nandy has suggested the decision on whether to hold a second independence...
The First Minister said a ballot could be held without Westminster's consent provided it's ruled as legal.
More than half of Scots would vote for independence - but they don't support a referendum this year.
MSPs voted by 64 to 54 for the principle of a referendum but Boris Johnson refuses to allow one.
The Labour leadership contender said he wanted a new constitutional set-up 'based on federalism'.
Some MPs cheered as royal assent was confirmed for the European Union (Withdrawal Agreement) Act.
The First Minister's spokesman said she remains 'committed' to holding a vote this year.
The Prime Minister said a new independence vote would cause continued 'political stagnation'.
The shadow business secretary says independence would be for the people of Scotland to decide.
Ex-justice secretary Kenny MacAskill - and newly-elected MP - said a longer wait is 'no bad thing'.
Holyrood backed the Referendums (Scotland) Bill at its final stage by 68 votes to 54.
The First Minister has called for the Prime Minister to 'agree and negotiate' the transfer of powers to Holyrood to hold indyref2.
The Ross, Skye and Lochaber MP has been unanimously re-appointed at the parliamentary party's AGM.
The First Minister said there is 'growing cross-party recognition' the question of a second vote should not be decided at Westminster.
The First Minister will invite people in Scotland to come together to back another referendum.
The SNP Westminster leader said the general election 'reaffirmed the mandate' for a referendum.