In a meeting chaired by President Hamid Karzai, the National Security Council "condemned" increasing numbers of "rocket attacks (by the) Pakistani military against the country", a statement from the presidential palace said.
It said the attacks were "aimed at disrupting the second round of presidential elections", due to be held on June 14.
A spokesman for the Afghan Ministry of Defence, Mohammad Zahir Azimi, said "Pakistani helicopters" had crossed the border and flown over the eastern province of Kunar.
The National Security Council said it would "raise serious concerns" with Pakistan through the foreign ministry, according to the statement.
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In protest, Afghan security officials will not participate in a regional security summit due to take place in Islamabad on June 4.
The council also took issue with the lack of reaction from the United States, describing the silence as "a violation of (the) long-term strategic pact signed between the two countries".
In the 1990s, Islamabad helped nurture the rise to power of the Taliban in Afghanistan and was one of the only countries to recognise the regime, which ruled from 1996 to 2001.