Eight people, most of them women, were also wounded by the rocket fire - one of three cross-border raids that took place about the same time overnight.
Pakistani officials denied the allegations.
Speaking to Al Jazeera, Athar Abbas, a Pakistani military spokesman, said: "[Pakistani forces] only fired at the militants who were observed in the border area, so I don't know how they are claiming that we fired on the camps or the bases of Afghanistan.
"That's not correct."
Hamid Karzai, the Afghan president, held an emergency meeting in the wake of the incidents.
Nato bases targeted
Dan Nolan, Al Jazeera's correspondent in Afghanistan, said there were definitely two rockets attacks on Khost.
One of those attacks killed three civilians; another attack targeting Nato and Afghan army bases killed one civilian, he said.
An Afghan defence ministry spokesperson told Al Jazeera that both the attacks came from the Pakistani side of the border.
Nato said one attack originated at least 300m on the Pakistani side of the border, and killed three Afghan civilians.
In a separate incident, a rocket fired from Pakistan hit a hospital in the northeastern Afghan province of Kunar.
One man was killed and a man and woman were wounded in the attack, the provincial governor said.
On the eastern province of Patkika, three artillery shells fired from Pakistan landed inside an Afghan army camp and three more landed close to a base of the Nato-led force in the country.
Nato officials said their forces returned the fire and no casualties were reported.
Some Afghan defence officials have accused the Pakistani military of turning a blind eye and allowing Taliban fighters on the Pakistan side of the border to launch these attacks, a claim that the Pakistani military force say is not true.
Karzai touched off a diplomatic storm recently when he said: "Afghanistan has the right of self-defence. When they cross the territory from Pakistan to come and kill Afghans ... it gives us the right to go back and do the same."