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Sharp currency falls and economic turmoil gripping the country after the group's takeover of Kabul two weeks ago would subside, Reuters cited the Taliban as saying.
Zabihullah Mujahid, the group's main spokesman, condemned an overnight US drone strike against ISIS militants following Thursday's suicide attack near the airport as a “clear attack on Afghan territory".
But he appealed to the US and other western nations to maintain diplomatic relations after their withdrawal, which he expected would be completed “very soon".
The exact timing of the formation of a new Cabinet remained unclear.
Reports originally quoted Mr Mujahid as saying the announcement would be made in the coming week, but in a voice message later he said the make-up of the new Cabinet would be cleared “in one or two weeks".
Responding to a question about whether any women would be included in the new Cabinet, he said this would be a matter for the leadership to decide and he could not anticipate what their decision would be.
There is mounting frustration in Kabul at the severe economic hardship caused by a plummeting currency and rising food prices, with banks still shuttered two weeks after the fall of the city to the Taliban.
On Saturday, a statement from the Taliban said that banks were ordered to reopen with a weekly limit on withdrawals of $200 or 20,000 afghanis.
Mujahid said officials had already been appointed to run key institutions including the ministries of public health and education and the central bank.
UN officials have given warnings that Afghanistan faces a humanitarian catastrophe, with large parts of the country suffering from extreme drought conditions.
The economy, shattered after four decades of war, also faces the loss of billions of dollars in foreign aid, following the withdrawal of Western embassies from the country.
Mr Mujahid said the economic problems being experienced would be eased once the new government was in place.
“The fall of Afghani against foreign currency is temporary and it is because of the situation that suddenly changed, it will come back to normal once the government system starts functioning,” he said.