The former first minister, whose new party failed to win any seats in this month’s Scottish election, said politicians at Holyrood should be “forcing the issue”.
With the new Scottish Parliament having a majority of MSPs who support independence, he insisted the country had “never been stronger in political terms”.
In contrast, he said the position at Westminster had “never been weaker”.
His comments came in a message to Alba’s 5,500-plus members – with the party claiming new recruits have increased by 10% since the May 6 election.
It has already pledged to stand candidates in the 2022 council elections in Scotland, with the former SNP leader saying: “Local government is an area that we are going to be concentrating a great deal of attention.”
However he claimed that just two weeks on from the Holyrood vote, the “constitutional issue is already gradually slipping off the political agenda”.
Mr Salmond insisted: “Independence should be right up there, first and foremost, in terms of dealing with the pandemic, in terms of recovery and economic recovery from it.
“We should be talking about the constitutional question in Scotland, we should be forcing the issue because London has never been weaker and Scotland has never been stronger in political terms.
“But if we allow it to slip off the political agenda to allow the (Boris) Johnson Government to regain its political balance, then the chance may be missed, and may never come again.
“An absolute majority of the Scottish electorate, two weeks ago in the Scottish elections, voted for parties committed to Scottish independence, a mandate that is unarguable but one that has to be used because mandates that are not used can sometimes be lost.”