Major-General Abd al-Aziz Muhammad, director of the joint operation centre in the Ministry of Defence, said on Tuesday that the Iranian army crossed the Iraqi borders on April 21 and April 26.
"In the second violation, there was bombing against the positions of Kurdistan Workers Party (PKK)," he said.
"The Iranian troops reached five kilometres into Iraqi territories before they withdrew."
The spokesman said the ministry had sent the case to the foreign affairs ministry to settle it at the diplomatic level.
Iran has denied it made any incursion into Iraq or bombarded suspected positions of the Kurdistan Workers Party inside Iraq's autonomous Kurdish enclave.
The official Iranian News Agency, IRNA, quoted an unidentified political source as saying the reported attacks were "fabricated and prejudiced".
"Iranian armed forces are reasonable and wise when it comes to confronting desperate moves by terrorist groups on Iran's border," the Iranian political source said, adding: "Iran will carry out what is necessary to ensure security there."
Witnesses in the Kurdish enclave in northern Iraq said on Monday the attacks against the PKK, whose leader Abdullah Ocalan is serving a life sentence in Turkey, were concentrated on villages in the province of Kalaa Dazza, 100 miles north of al-Sulaimaniya, near the Iranian border.
Iran has denied the claim that
it bombarded Iraqi territory
The bombardment was mainly concentrated on the villages of Razka, Jukhanki and Shanawa, where the PKK, which is banned in Iran and Turkey, is suspected to have offices and positions.
The attacks set off fires and inflicted serious material damage on the four villages.
Aljazeera's correspondent in northern Iraq, Ahmad al-Zawiti, visited the village of Razka on the Iraq-Iran border and documented some reactions from officials and residents.
Ali Hamad Su, Kalaa Dazza district commissioner, said: "Iran has no right to violate the sovereignty of Iraq under any pretext and since it is a neighbouring country, it must maintain this sovereignty."
Signs of bombing
Al-Zawiti said it took Aljazeera's team more than three hours to cover 10km of rough mountain roads to reach the bombing site.
"Signs of bombing could be clearly seen," he said.
"The area contains the Qandil mountains, which act as a shield for fighters of the KPP in their clashes with the Iranian army.
A shepherd said: "One of the rockets fell on my sheep and killed some."
Another resident told Aljazeera: "About 60 rockets have fallen on our village as if we were in a war."