Under the new agreement, Abdullah will introduce members of his team to the president to be included in the cabinet. The US-Taliban pact was signed on 29 February.
Dostum, a notorious former warlord, is accused of ordering the torture and rape of a political rival in 2016.
"As long as there is no sustained reduction in violence and insufficient progress towards a negotiated political settlement, Afghanistan will remain vulnerable to terrorism", Pompeo said.
Nato, which maintains a training mission in Afghanistan, issued a similar message.
Ghani and Abdullah held parallel inauguration ceremonies in March.
It was not immediately clear whether Sunday's agreement would result in the aid commitment being reinstated. The Pentagon has confirmed a strong uptick in the number of Taliban attacks against Afghan security forces in recent weeks.
"I welcome the decision taken by Afghanistan's political leaders to resolve their differences and join efforts to form an inclusive government", Stoltenberg said in a statement.
After election officials in December declared Ghani the victor by a large enough margin to avoid a runoff vote, Abdullah declared himself president, although the global community recognized Ghani's victory.
In his previous visit to Kabul earlier this year, Pompeo announced a $1 billion cut in U.S. aid to the war-ravaged country over the political standoff between Ghani and Abdullah.
He called the bombing retaliation for statements blaming the group for an attack elsewhere in the country on Tuesday, in which at least 56 people were killed, including 24 mothers, newborn babies and nurses at a maternity ward run by Doctors Without Borders (MSF).
At least three crazed gunmen disguised as police officers ran amok through the clinic run by the global humanitarian organisation Doctors Without Borders in the Afghan capital Kabul.
Mujahid added that it would be better to work in earnest to consolidate peace in Afghanistan instead of resorting to subterfuge and empty words, stressing that all Afghan factions should pave the way for this process in order to find a solution to the Afghan problem.
US President Donald Trump has made leaving Afghanistan a priority.
The change in posture for the Afghan military comes months after they pledged to only react defensively to any Taliban attacks.
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