Karzai had indicated earlier in the week that he had judged the August 20 date set by the election commission to be unconstitutional, Bays said.
The US state department said that it supported the "underlying principles" of Karzai's decision but thought that an August date would best ensure safety and a fair poll.
Opponents of the president have said the move "may just be an effort by Karzai to use his advantage as president to wrong-foot them and use his office to help his campaign [for re-election]," he added.
"The former finance minister, Ashraf Ghani, told me earlier that the president should not set the election date, but the Independent Election Commission. He also said that if there is any dispute, then it is not up to the president to judge."
Dawood Sultanzoy, an Afghan MP and a presidential candidate, said that Karzai had read the constitution in such a way as to suit his personal ambitions.
"The president is using the constitution as a cafeteria - whenever he chooses, he wants to pick those articles out and side with them," he said.
"He very conveniently forgot article 59 of the constitution which says that any individual who abuses the trust and the sovereignty of the people for his own interests is in violation of the law."
Karzai's move comes amid a deterioration in relations between Washington and Kabul, ostensibly over how to tackle opposition fighters linked to the Taliban, al-Qaeda and tribal leaders.
"Karzai has been in charge for more than seven years and I think some international figures see him as part of the problem rather than part of the solution," Bays said.
"When Richard Holbrooke, the US special representative to Afghanistan and Pakistan, came to Kabul, he met Karzai – but he also met many of the challengers to be the president. Holbrooke made it clear that the US does not have a preferred candidate."
Speaking last week to Al Jazeera, the Afghan president said that Barack Obama, the new US president, had not contacted him during the first month of his term.
The Afghan constitution says the election should be held within 30 to 60 days before the end of the presidential term on May 21.