"40 Taliban terrorists were killed, 12 were injured and 13 hideouts and enemy positions were destroyed", the bodies said in a joint press release, published by the Defense Ministry on Twitter.
It added that the Taliban and their regional allies are pursuing power through the "imposed war", but the Afghan government will defend every inch of its territory.
When Senator Jeanne Shaheen asked Pompeo to ensure that the deal between the Taliban and the United States protects the rights of the Afghan women, Pompeo said, "Remember, the Afghans will ultimately decide".
Mohammad Yusouf Ayubi, head of the provincial council in Kunduz, said at least six people were killed and more than 50 were wounded as the insurgents attacked from multiple directions just after midnight.
The bloodshed comes as the U.S. pushes for a peace settlement with the Taliban, and ahead of a new round of talks expected to take place in Qatar later this month.
He said the call for more fighting will not advance peace efforts and that "if executed, it will only yield more suffering and thousands more causalities".
The deadly attack came hours after the Taliban outfit announced launching its annual offensive dubbed "al-Fath" which means "victory" in Arabic language.
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The Taliban effectively controls almost half of Afghanistan and has continued to launch frequent attacks on security forces despite holding several rounds of peace talks with the United States in recent months after almost 18 years of war.
Earlier in the day, a local security official said, as cited by Khaama Press that the Afghan security forces killed nine members of the Taliban movement in the southern Afghan province of Kandahar late on Friday after the militants tried to overrun a security checkpoint.
Afghan President Ashraf Ghani's office on Saturday condemned "in the strongest words" the announcement of Operation Fath. The US is hoping to seal a draft agreement on counter-terrorism assurances, troop withdrawal, intra-Afghan dialogue, and a comprehensive ceasefire, before Afghan voters go to the polls in July.
"The continuation of war is no one's interest", it said.
The Taliban has long refused to speak officially with Kabul, dubbing the government a "puppet" of the West, and the group has insisted that government officials are attending only in a "personal capacity".
The spring offensive traditionally marks the start of the so-called fighting season, though in reality fighting in the last winter has continued unabated. "We assemble the Resolute Support leadership together and Gen. Miller said the Taliban have made it clear that they have ignored the will of the people and have guaranteed more violence", Butler said.
But on Monday three US Marines were killed in a Taliban blast at Bagram air base north of the city, and authorities in the capital are on high alert for new attacks.