Two babies and 12 mothers and nurses were killed when several gunmen stormed the hospital on Tuesday morning.
Meanwhile, in the eastern province of Nangarhar, a bombing at a funeral killed at least 26 people.
Mr Pompeo said: “Any attack on innocents is unforgiveable, but to attack infants and women in labour… is an act of sheer evil.”
“Terrorists who attack mourners lining up for prayer at a funeral are only seeking to tear apart the bonds that hold families and communities together, but they will never succeed.”
He added: “During the holy month of Ramadan and amidst the threat of Covid-19, these dual attacks are particularly appalling.”
In the wake of the attacks, President Ashraf Ghani said he was ordering the resumption of offensive operations against the Taliban and other groups.
He accused the militants of ignoring repeated calls for a reduction in violence.
The Islamic State (IS) group said it was behind the attack on a police commander’s funeral in Nangarhar, in the east of…