Nicola Sturgeon told MSPs a target to reduce six week delays in discharging patients had been delivered.
But Labour said it had not been met for more than three years, and called for her to amend the record.
Ms Sturgeon's office said she would not be revising her remarks because the six-week target had been met in the past.
Delayed discharge - sometimes referred to as bed blocking - is when a patient is not released from hospital despite being clinically well enough to be discharged, often because of a lack of care of care services.
Ms Sturgeon faced criticism over the issue during first minister's questions in the Scottish Parliament, with Scottish Labour leader Kezia Dugdale saying that people had remained in hospital for a total of 612,000 days last year when they were well enough to go home.
She said Ms Sturgeon had told the SNP conference in 2011 that patients spent 200,000 days in a hospital bed when they did not need to.
Ms Dugdale added: "That means it has more than trebled under the SNP government since this first minister admitted there was something badly wrong. So, by any measure that is unacceptable.
"That is thousands of patients, the majority of whom are elderly, ready to go back home or into the community but can't because the extra support they need just isn't there."
She also claimed that delayed discharge got worse during the peak of summer despite Health Secretary Shona Robison saying in February that she wanted to "completely eradicate" the problem.
The substance is this. In the middle of a flood of stats, Ms Sturgeon said: "Having delivered the target of zero delays over six weeks, we have progressively toughened that target."
A delay of that duration, for the avoidance of doubt, involves a patient being kept in hospital for at least six weeks longer than clinically necessary, generally because no alternative care is available.
Dr Simpson said he had checked with parliament's own information centre. Based on that research, allied to his own knowledge, he believed the First Minister's remarks were misleading.
According to Labour, Scotland's patients had not enjoyed "zero delays over six weeks" for three years. That is, there had been patients during that three-year period who had stayed more than six weeks in hospital beyond potential discharge.
The immediate response from the First Minister's office is that the target - of zero delays over six weeks - had been met in the past. The general tenor of her remarks was that matters were improving - while there remained more to be done.
Dr Simpson has now, in effect, suggested that Ms Sturgeon might reconsider that stance.
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Ms Sturgeon responded by acknowledging that there was still work to do, but said "real progress" was being made.
She later added: "Since 2007 there's been a 52% reduction in delays over four weeks, a 55% reduction in delays over six weeks, the number of delays over three days is down by 50%, the number of delays over four weeks has been reduced as well.
"Having delivered the target of zero delays over six weeks, we've progressively toughened that target and we're now focusing on ensuring patients are discharged within 72 hours."
That comment drew an angry response from Labour MSP Dr Richard Simpson, who subsequently made a formal point of order to the presiding officer.
Dr Simpson said that the six-week target had been missed in every month since 2012.
He also said that official statistics showed that more than 4,700 patients had been delayed more than six weeks despite being fit to leave since 2012, and nearly 400 in the past two months alone.
Dr Simpson added: "We all know that nationalist rhetoric is divorced from reality but this is completely unacceptable.  It was completely wrong to claim that these targets had been met when in reality thousands of patients had waited in hospital beds.
"Our NHS is in real trouble. The health minister pledged to abolish delayed discharge by the end of the year. Instead it is going in the wrong direction. Meanwhile we see the first minister is making completely false claims about her government's record.
"Patients and staff don't benefit from bogus claims about NHS performance. The first minister should correct the record, and this SNP government should get a grip of delayed discharge rather than bury their heads in the sand."
But a Scottish government spokeswoman said: "The first minister was correct that the old six week target was met, on a number of occasions, under this government.
"Subsequently, the Scottish government introduced new tougher targets that no patient should wait more than four weeks, and later two weeks, from when they are clinically ready for discharge.
"Working with our partners in local government we've made the level of performance we expect tougher still, with an ambition for patients to be delayed for no more than 72 hours."
Labour has accused the Scottish first minister of misleading parliament over hospital bed blocking statistics.