Galbraith had been particularly critical of the August 20 vote, which was marred by allegations of widespread fraud.
Preliminary results from the election gave Hamid Karzai, the presidential incumbent, a 54.6 per cent share of votes cast.
But a UN-backed fraud watchdog ordered an audit of the results from 12 per cent of polling stations, where suspiciously large numbers of votes were cast, or where one candidate received 95 per cent.
If enough of Karzai's ballots are nullified because of fraud that he no longer has 50 per cent, he would face a run-off election against Abdullah Abdullah, a former foreign minister.
Galbraith's comments on the veracity of the election results are thought to have angered Eide, his Norwegian boss.
Galbraith left Kabul for the US earlier this month after the two men quarrelled.
The dispute has exposed divisions among Afghanistan's Western backers over how to deal with the presidential election.
Western powers have sought to shore up their relationship over Afghanistan, with Anders Fogh Rasmussen, the secretary-general of Nato, vowing that troops would remain there for as long as necessary.
"Our operation in Afghanistan is not America's responsibility or burden alone: it is and it will remain a team effort," he said on Tuesday after meeting Barack Obama, the US president.
|Obama and Rasmussen, left, met to discuss Nato's role in Afghanistan [AFP]
Obama said that Washington considers the war in Afghanistan as not just a US battle but "a Nato mission as well".
Nato-led forces have been struggling to contain a surge in attacks by the Taliban.
In the latest incident, a suicide car bomber attacked a convoy of foreign forces in southeastern Afghanistan on Wednesday, killing one American, officials said.
The attack occurred in the Mandozai district of Khost province, bordering Pakistan, as the convoy crossed a bridge.
"One of the cars belonging to the troops is on fire and there are some casualties among them, but at this stage I have no precise information," said Wali Shah, a district chief.
He said that a foreign helicopter could be seen evacuating casualties.
In a separate development, the Afghan interior ministry said, that more than 20 Taliban fighters had been killed in an operation in the western part of the country.
General Stanley McChrystal, the senior US and Nato commander in Afghanistan, has said that the military effort risks failure unless more troops are sent to the country as part of a revised strategy.
While Obama has said he is yet to make a decision on sending more troops to Afghanistan, McChrystal is expected to ask for an additional 30,000 to 40,000 troops for combat operations and training of Afghan forces.
The UN's Eide has also called for more troops to help train Afghan security forces.