Asked for evidence for this claim, Mr Key said his answer was based on formal advice from the Inland Revenue Department (IRD). He said he would be "very, very surprised" if enrolment rates changed after the subsidy was removed.
Mr Robertson said Budget documents released yesterday showed "the exact opposite" of what Mr Key told Parliament.
IRD officials advised in a regulatory impact statement that removing the subsidy would lead to a fall in subscribers to the scheme.
Under a section titled "likely impacts", the briefing paper predicted "lower numbers of Kiwisaver members (particularly among the self-employed and children)".
This was the only reference to enrolment numbers in the 20-page document.
A month after the Budget, New Zealand's largest Kiwisaver provider ANZ Bank reported that enrolments had fallen by more than half.
Instead of reflecting the IRD advice, Mr Key "made a blanket statement claiming the IRD backed his position", Mr Robertson said.
"The Prime Minister has a fundamental requirement to tell the truth to Parliament," he said.
"Blatantly misrepresenting advice he receives brings the integrity of Parliament into question."
Speaker David Carter will now decide whether the complaint should be referred to the Privileges Committee.
Government scrapped the kickstart payment because Kiwisaver already had 2.5 million members and ministers felt it no longer needed a sign-up perk.
Getting rid of the subsidy was expected to save around $125 million a year.
A spokesman for the Prime Minister said he stood by his comment.
A briefing paper prepared for Cabinet a month after the IRD advice said removing the kickstart payment was "likely to have only have a limited effect (if any) on enrolment rates in Kiwisaver" because other subsidies and employer contributions remained in place.
