Tommy Sheridan of the Scottish Socialist Party accused McConnell of "avoiding the question" after he refused to allocate blame to either side in the dispute.
But McConnell said the parties should start negotiating locally and nationally to resolve the dispute.
As Children Now went to press, nine of Scotland's 32 local authorities had reached a pay settlement with nursery nurses.
Officials from Unison's UK headquarters attended a rally in support of the striking workers in Glasgow last week.
But they were attacked by councillor Frank Russell, chair of the employers' side of the Scottish Joint Council.
"It is bizarre that the general secretary and president of Unison are up in Scotland at a rally seeking the Executive's intervention when pay and grading is dealt with at the local level in England and Wales," he said.
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