The Justice Secretary insisted the centuries-old requirement was a "legal barrier which stands in the way of too many cases going forward to court" when there would be prosecutions in other countries.
Scrapping the "complex" legal rule, which means evidence against a person in a criminal case must come from more than one source , is "vital", he added.
Mr MacAskill spoke out on the issue the day before a key vote on the proposal, which is included in the Scottish Government's Criminal Justice (Scotland) Bill.
Plans to abolish corroboration have been welcomed by the police, victims' groups and prosecutors, with some arguing that removing the need for corroboration will make it easier to take cases of sexual assault and domestic abuse to court.
The Crown Office found that in 2012-13 there were 2,210 domestic abuse cases which could not be prosecuted because of insufficient admissible evidence.
But there has been fierce opposition from within the legal profession to the abolition of corroboration.
The Justice Secretary has already announced a special group is being set up, chaired by former High Court judge Lord Bonomy, to consider what safeguards would be needed if the change is passed
The Scottish Parliament will debate the general principles of the Bill tomorrow, with Mr MacAskill hailing the legislation as a "package of significant reforms to modernise our criminal justice system".
He added: "The Bill includes the proposal to abolish the corroboration requirement and remove a legal barrier which stands in the way of too many cases going forward to court, cases that would proceed elsewhere.
"No other comparable criminal justice system, including all the 47 states that are signed up to the European Convention on Human Rights (ECHR), operates a general requirement for corroboration.
"This means that Scotland's legal system, as it currently stands, is denying access to justice to possibly thousands of victims a year."
The Justice Secretary was visiting the ASSIST organisation in Glasgow, which helps victims of domestic abuse.
Mr MacAskill praised the group for "doing great work to improve support to the victims of domestic abuse while also working with Police Scotland and the domestic abuse court to ensure that the evil perpetrators of such crimes are caught and made to face the consequences of their actions".
He added: "The fact remains that until the requirement for corroboration is abolished too many domestic abuse cases and other crimes committed behind closed doors will be prevented from proceeding to court - denying victims their opportunity to have their day in court and access to justice.
"We have a duty to provide an effective justice system to these victims, indeed all citizens, not just those whose cases happen to meet complex corroboration rules.
"That is why it is vital for our reforms to go ahead, with the appropriate safeguards which will be examined through Lord Bonomy's group."
Mhairi McGowan, head of service at ASSIST, said: "The current justice system is failing victims.
"Credible allegations are being made, yet with the system based on corroboration there is not the opportunity to test those allegations in court.
"The criteria for prosecution should be the quality of evidence available. We see clients confused and despondent, and we have a duty to answer their criticisms."