
The SNP leader said the turmoil caused by the Prime Minister demonstrated why a Labour Government in Holyrood would be "ineffective".
Mr Swinney accepted Scottish Labour leader Anas Sarwar's chances of becoming first minister had been "severely damaged" by the scandal surrounding Peter Mandelson's appointment as ambassador to the US.
Lord Mandelson was sacked from the role in September after new details emerged about his connection to paedophile financier Jeffrey Epstein, but it emerged last week that the peer had been appointed to the role despite failing UK Security Vetting.
Speaking to journalists in Edinburgh, Mr Swinney said that in contrast to the "chaos" offered by Labour, he offered "reliable, experienced leadership".
"Right at the very heart of this election campaign is the question of leadership," he said.
"I offer reliable, trusted and experienced leadership on behalf of the Scottish National Party."
In contrast, he said: "If we've got one chaotic Labour government already, why on earth would we choose another?"
Pressure is growing over the Prime Minister's leadership, however he has insisted he was not told Lord Mandelson failed vetting.
Sir Olly Robbins, the former top Foreign Office civil servant sacked in the wake of the scandal, told MPs he felt pressure from Downing Street to expedite the process.
While the Scottish Labour leader, and Holyrood election candidates, have called for Sir Keir's resignation, just two Scottish Labour MPs have done so - Brian Leishman and Euan Stainbank.
Speaking about the lack of comment from Scottish Labour MPs, Mr Swinney said: "I think they are just, they have been empty vessels since they got into Westminster two years ago.
"Empty vessels. So they demonstrate that voting Labour gets you absolutely nowhere."
Mr Swinney said there was a "political impotence" around the decision to appoint Lord Mandelson.
He added: "The United Kingdom, Labour, Government is absolutely consumed by one thing, and that is the Mandelson scandal and the survival of one individual: the Prime Minister and the saving of the Prime Minister's job.
"So while the SNP is focused on practical action to support people in dealing with the cost of living, the UK Government is focused on the Prime Minister alone."
The SNP leader said: "I think Keir Starmer has severely damaged the Labour election campaign in Scotland because he has proved a point that I've been making, that Labour governments are ineffective. They don't work very well.
"And we've been told 'wait for a Labour government at Westminster, everything will get better'.
"Well, look, it's appalling, it's chaos, it's a shambles."
He said the Prime Minister's actions were "totally and utterly damaging" to the process of government.
Meanwhile, Mr Sarwar has doubled down on his calls for the Prime Minister to resign, but has attempted to distance the Holyrood election campaign from Westminster.
The Prime Minister was in Scotland visiting the Faslane naval base at the weekend, but avoided joining candidates on the campaign trail, making him the only leader of a UK party to do so.
Mr Sarwar said: "A vote for Scottish Labour in this election is not an endorsement of Keir Starmer or a UK Labour government."
He added it was not an election to "pass judgement" on a government that had been in power for just two years, while the SNP have led in Scotland for almost 20.