A rocket fired from Pakistan hit a hospital in the northeastern Afghan province of Kunar in a separate incident.
One man was killed and a man and woman were wounded in the attack the provincial governor said.
Three artillery shells fired from Pakistan landed in an Afghan army camp and three more landed close to a Nato base in the eastern Afghan province of Paktika, alliance officials said.
Nato forces returned fire. No casualties were reported.
Arsala Jamal, the Khost governor, said: "We have very clear evidence and we have checkpoints there have confirmed that these rockets were launched from Pakistan aimed especially at Khost."
Athar Abbas, a Pakistani military spokesman, said: "They 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."
Dan Nolan, Al Jazeera's correspondent in Afghanistan said there were definitely two rockets attacks into the Afghan province of Khost. One of those attacks killed three civilians another attack killed one civilian targeting Nato and army bases.
Hamid Karzai, the Afghan president, 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."
Some Afghan defence officials had 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 said is not true.
One Afghan defence ministry spokesperson told Al Jazeera that both of the attacks came from the Pakistani side of the border but Nato says only one attack that killed three civilians was fired from Pakistan, at least 300m on their side of the border.