The Scottish National Party had argued that its Commons leader enjoyed the support of more MPs than Labour leader Jeremy Corbyn.
There are currently 54 SNP MPs but only 40 of Labour's 229 MPs expressed support for Mr Corbyn on Tuesday.
Speaker John Bercow said he had sought expert advice.
He said Labour "currently constitutes" the official opposition and its leader is recognised by the Speaker "for statutory and parliamentary purposes" as the leader of the opposition.
Mr Bercow was replying to a point of order raised by SNP MP Pete Wishart, who told the Speaker that Labour had lost two-thirds of its shadow cabinet and its leader no longer commanded the majority of his backbench MPs.
The SNP MP said: "It can now longer provide shadows for large departments of State. It is in clearly in no shape to assume power and meet these key responsibilities and obligations as outlined in Erskine May (the parliamentary rulebook)."
The SNP said it would be able to fill all of the relevant shadow posts to the government.
Mr Corbyn has still not appointed a shadow Scottish secretary.
The previous incumbent, Ian Murray, has not been replaced after becoming one of more than 20 members of Labour's shadow cabinet to quit earlier this week in an effort to force Mr Corbyn to resign.
Mr Corbyn subsequently lost a vote of no confidence by 172 votes to 40 but said the ballot had "no constitutional legitimacy" and that he would not "betray" the members who voted for him by resigning.
His allies have challenged Mr Corbyn's critics to trigger a formal leadership contest if they want to replace him.
Earlier, Labour's shadow chancellor John McDonnell - who has remained loyal to Mr Corbyn - said the SNP would "always play a few stunts and you can't blame them for that".
The SNP won 56 seats at last May's election, but Michelle Thomson and Natalie McGarry have since withdrawn from the party whip amid police investigations.
The SNP's attempt to be made the official opposition at Westminster has been rejected by the Speaker of the House of Commons.