Abdullah Abdullah's comments come ahead of a September deadline for the government to honour the fragile agreement signed after the fraud-tainted presidential election in 2014, which both leaders claimed to have won.
By then the government is expected to enact sweeping election reforms and amend the constitution to create the position of prime minister for Abdullah. Observers say that deadline is unlikely to be met, effectively tipping Afghanistan into a political crisis.
"Mr President, over a period of three months you do not have time to see your chief executive face-to-face for even an hour or two? What do you spend your time on?
"There are arguments in every government but if someone does not have patience for discussion, then he is unfit for the presidency."
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The acrimony comes as Taliban insurgents are threatening to overrun Lashkar Gah, capital of the strategic poppy-growing southern province of Helmand.
The presidential palace offered a measured response today, saying Abdullah's remarks "were not in accordance with the spirit of governance", while at the same time extending him an olive branch.
"The National Unity Government will work collectively, and very soon serious and effective discussions will take place (regarding Abdullah's comments)," the palace said, without offering details.
Abdullah said he would meet Ghani tomorrow to try to iron out some of their differences.
Their power-sharing deal, brokered by US Secretary of State John Kerry, was hailed after the troubled 2014 election as a breakthrough as it averted potential military and political confrontations.
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