The air strike targeted Islamic state hideouts in the Hask Mina district. The dead commanders are identified as Qari Esrar and Mullah Hasghar.
The report of the air strikes came after the killing of at least nine civilians in an overnight operation by Afghan security forces outside the Nangarhar provincial capital of Jalalabad. The victims included relatives of the speaker of the Senate, Fazl Hadi Muslimyar, the office of the provincial governor said in a statement.
Eight people were injured, in addition to the nine killed in the operation in Chapahar district. Some local people put the death toll at 12, with 28 wounded. The incident underlines the daily risks Afghan civilians face as fighting has intensified since the Taliban launched its annual spring offensive last month.
Top Islamic State commander in Afghanistan killed in airstrike: officials
The latest figures from the United Nations Assistance Mission in Afghanistan show 763 civilians were killed and 1,495 wounded in the first three months of the year, a similar level to the corresponding periods of the two previous years.
The violence has spread across Afghanistan in recent weeks with heavy fighting in provinces from Badakhshan, Baghlan and Faryab in the north to Farah in the west, where the Taliban briefly threatened to overrun the provincial capital, and Ghazni in the centre.
Officials said that a district centre in Uruzgan province, on a key transit route from the drug producing regions of Helmand and Kandahar, was under serious threat. Security forces in Chora district in the middle of the province had abandoned the governor's compound and police headquarters but fighting continued, said Hayatullah Fazli, a member of the provincial council.
The provincial governor's office confirmed the fighting but denied reports that the district, which has seen heavy fighting in recent days, had fallen. The insurgents have put out videos of Afghan soldiers captured in the district urging others not to fight against the Taliban.
With additional input from Reuters.
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