Indian Foreign Secretary Vijay Keshav Gokhale called the strike a "non-military pre-emptive action, specifically targeted at the Jaish-e-Muhammad camp".
Modi had threatened a "jaw-breaking" response to the February 14 attack.
The military action comes a week after Pakistan militants killed 42 Indians in a suicide attack.
Balakot police chief Saghir Hussain Shah told the Associated Press that the bombs had been dropped on a sparsely populated forest area.
The Pakistani spokesman said there were no casualties or damage.
Pakistan's Foreign Minister Shah Mehmood Qureshi said that better sense should prevail in India, and that Islamabad would respond in kind to any "misadventure".
Pakistan Air Force jets were scrambled in response to the incursion, Ghafoor said.More news: Are Samsung, Huawei's foldable smartphones worth the hefty price tag?
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"Acting on intelligence, India early today struck the biggest training camp of Jaish-e-Mohammad in Balakot", he said.
"Credible intelligence was received that JeM (Jaish-e-Mohammed) was attempting another suicide terror attack in various parts of the country, and the fidayeen jihadis were being trained for this objective". In a tweet Tuesday, he said, "Indian aircrafts intruded from Muzafarabad sector".
Insurgents have been demanding either outright independence or union with Pakistan.
"The Australian government urged India and Pakistan to exercise restraint, avoid any action which would endanger peace and security in the region and engage in dialogue to ensure that these issues are resolved peacefully", a statement from the Australian Ministry for Foreign Affairs read.
Muhammad Amir Rana, a security analyst and executive director of the Islamabad-based Pakistan Institute of Peace Studies, urged the global community to move quickly to de-escalate tensions.
Kashmir - divided between India and Pakistan but claimed by both in its entirety - has been the cause of two wars between the uneasy neighbors. India has demanded that Jaish-e-Mohammad's leader, Azhar Masood, be listed as a terrorist by the United Nations, but that has been stymied by China.
The military spokesperson said that the Indian objective was to target civilians and then project them as terrorists - something that Modi wanted to use to gain political mileage for the upcoming election.
It says Rahman was influenced by extremist Mullahs in Pakistan and decided he would go to Jihad in support of the Taliban.