On Saturday SNP president Mike Russell said he did not think independence could be achieved “right now”.
Mr Blackford, who stood down in December, was asked on BBC Radio’s Good Morning Scotland if he agreed with Mr Russell’s assessment.
He told the programme: “We are facing what is a very challenging period.
“Political parties that are not united face, of course, electoral challenges.
“I think it is really up to us about how we respond to the period that we have come through.”
The Ross, Skye and Lochaber MP said support for independence was still “hovering round about or close to the 50% level”.
He added: “We need to demonstrate that we are worthy of the trust of the people and its about the Scottish government delivering across all the devolved areas.”
Mr Blackford said he believed new First Minister Humza Yousaf “would surprise people” and said he had put together an “exciting cabinet of talent”.
He also dismissed a call from SNP MP Angus MacNeill for the party’s leadership contest to be re-run following the turbulent events of last week.
Mr Blackford said: “I think people are very satisfied that we have a process that has delivered a result and that we have a leader that we can fully get behind.”
He was speaking after Mr Russell admitted recent weeks had been “wearing” for the SNP, which recently selected Mr Yousaf to succeed Ms Sturgeon as party leader.
The party’s chief executive told The Herald newspaper: “In my 50-year association with the party this is the biggest and most challenging crisis we’ve ever faced, certainly while we’ve been in government.”
Meanwhile, Mr Blackford was also asked about a call from Scottish Conservative leader Douglas Ross for tactical voting to defeat the SNP.
Speaking to the Sunday Telegraph, Mr Ross said “where there is the strongest candidate to beat the SNP, you get behind that candidate.”
The UK Conservative party later rejected the suggestion from its leader in Scotland that voters could tactically back Labour to oust the SNP.
A Tory party spokesman said: “We want people to vote for Conservative candidates wherever they are standing as that’s the best way to keep Labour and the SNP out.”
Mr Blackford compared the comments to the cross party alliance against Scottish independence in 2014.
He told Good Morning Scotland: “I think what really Douglas has done is that he has demonstrated that Better Together is alive and well and it is a real fight for Scotland’s future.
“We want to make sure that we remove the risk of Conservative governments forever and the only way of doing that is by making sure that people do back the SNP in the next election.”
Why are police investigating the SNP?
Last Wednesday Mr Murrell was arrested by Police Scotland officers investigating SNP finances.
Officers searched the home he shares with Ms Sturgeon and the SNP’s headquarters in Edinburgh.
At the weekend it emerged a third address, reported to be Mr Murrell’s mother’s home in Dunfermline, Fife, was also searched.
The Scottish Mail on Sunday reported this part of the investigation resulted in the seizure of a luxury motorhome but Police Scotland declined to comment.
The force launched an investigation in July 2021 after complaints about how SNP donations were used.
The funds were donated for a new independence referendum campaign.
The SNP raised £666,953 through referendum-related appeals between 2017 and 2020.
Nicola Sturgeon said she was “not concerned” and “every penny” would be spent on the independence drive.
Questions were raised after SNP accounts showed just £97,000 in the bank at the end of 2019, and total assets of about £272,000.
Mr Murrell, who has been married to Ms Sturgeon since 2010, resigned last month after taking responsibility for misleading statements about a fall in party membership.
Last year it emerged that he gave a loan of more than £100,000 to the SNP to help it out with a “cash flow” issue after the last election.
The party had repaid about half of the money by October of that year.
At the time an SNP spokesman said the loan was a “personal contribution made by the chief executive to assist with cash flow after the Holyrood election”.
He said it had been reported in the party’s 2021 accounts.
Weeks earlier, MP Douglas Chapman had resigned as party treasurer saying he had not been given the “financial information” to do the job.