The attacks happened in the village of Datta Khel, North Waziristan, where army has been mounting an offensive against militant strongholds since June.
"During a search operation seven terrorists were killed in Datta Khel. Three soldiers including an officer also embraced martyrdom," an ISPR statement said on Sunday.
Four soldiers were wounded in an exchange of fire, it added.
A security official also confirmed the incident but told AFP that the number wounded in the attack was greater - estimating at least 11 soldiers were injured.
Ahmadullah Ahmadi, a spokesman for militant commander Hafiz Gul Bahadur, claimed responsibility for the attack.
Bahadur, a prominent local warlord once seen as "pro-Pakistani", is reportedly unhappy with the military offensive in North Waziristan.
"We carried out this attack because the army has established new check posts here," Ahmadi in a telephone call told AFP.
A separate military statement said Pakistani jets bombed insurgent hideouts in Datta Khel on Sunday, killing 27 militants.
"In precise aerial strikes, 27 terrorists including some of their important commanders and foreigners were killed in Datta Khel," it said.
Security officials have described the village as a stronghold of insurgent groups.
It is 40 kilometres (25 miles) west of Miranshah, the main town in North Waziristan.
Pakistan's semi-autonomous areas have long been a hideout for Islamist militants of all stripes - including al Qaeda and the homegrown Tehreek-e-Taliban Pakistan (TTP), as well as foreign fighters such as Uzbeks and Uighurs.
It was not possible to independently verify the casualties as media are banned from the area.
Pakistani jets and artillery began targetting rebel strongholds in North Waziristan in mid-June and ground forces moved in on June 30.
The army says it has killed more than 1,100 militants and lost more than 100 soldiers since the start of the operation.
An AFP tally based on regular updates from the military puts the militant death toll at nearly 1,500, with 124 soldiers killed.
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