Alba has decided not to contest the forthcoming by-election in Rutherglen and Hamilton West.
The party, led by Alex Salmond, had previously called for a single "Scotland United" candidate to avoid splitting the pro-independence vote.
But Mr Salmond said he had been "rebuffed" and now wanted to give the SNP the chance to prove they could "fly solo".
The by-election was triggered by a recall petition after Margaret Ferrier was suspended from the Commons.
The 30-day suspension followed the MP's conviction for breaking Covid lockdown rules by travelling to London and speaking in the chamber while awaiting a test result. She then travelled back to Scotland by train after learning it was positive.
The BBC says a date for the vote in Rutherglen and Hamilton West has yet to be set, but the earliest-possible date is October 5.
Suspended
Ms Ferrier took the seat for the SNP in 2019 with a majority of 5,240, but was suspended by her party over her Covid rule breaches and was sitting as an independent when she was ousted.
The seat has frequently changed hands between the SNP and Labour, and is being seen as a key test of Labour's chances of reviving its fortunes in Scotland.
- An anti-King Charles poster has been "banned" in Scotland, prompting a new freedom-of-speech row.
The design by the Alba Party was rejected by media company Global, which controls more than 250,000 UK advertising sites, over fears it could cause offence.
The poster depicts the official image of the King, as he appears on postage stamps, crossed out by a red prohibition sign. The image is below the message: "It's time for an Independent Republic of Scotland."
It is the second time this month that Global has rejected one of Alba's poster designs, after a cartoon image of Rishi Sunak, depicted as a vampire sucking Scotland's oil, was also refused.
The Telegraph says Global claimed it was "slanderous" toward the Prime Minister.
Alba believed that a media company should not be able to control the political messages the public sees.
'Censorship' claim
Chris McEleny, general secretary of Alba, claimed that "censorship" in political advertising was now a growing concern.
But an e-mail to Alba from Global, which also owns radio stations such as LBC, Classic FM and Capital, said it had strict rules around political advertising.
It told Alba it would not carry artwork "deemed to be politically persuasive with the use of something that is likely to cause offence, likely to get complaints and likely to have to be removed/replaced".