At its recent meeting in Bratislava, Slovakia, the assembly called on Ukraine to ensure that upcoming presidential elections are "fair, free and transparent," and stated that Kuchma was "due to step down after his second term expires in October."
That appeared to fit in with the facts in that Kuchma, 65, has said he would not be a candidate in the elections, even if the constitutional court has declared he is eligible to seek a fresh mandate.
But Vassyl Baziv, the head of the president's administrative office, declared the statement to be "interference in the internal affairs of a sovereign country."
"When the president departs is an affair of President Kuchma and the Ukrainian people, and not of a a foreign parliamentary assembly," Baziv added. "Today, they are giving orders to Kuchma and tomorrow they will be giving orders to a new Ukrainian president."
The NATO assembly is made up of parliamentarians from the 26 member countries, and has no executive role.
Kuchma has sought to position Ukraine for membership in NATO and distance itself from the dominating influence of its larger eastern neighbor Russia, on which it relies for its energy supplies.
Ukraine is a member of the Partnership for Peace program that NATO has set up for Eastern European republics, and has staged a series of joint military exercises with the alliance.
In addition, Kuchma has been invited to attend the NATO summit meeting in Istanbul June 28 and 29.
However, he has been frequently criticized for his record on media freedom and human rights.