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 insurgents attacked a district headquarters in the eastern Nangarhar province late Friday, killing two police, said Attahullah Khogyani, spokesman for the provincial governor.
Over a dozen Taliban fighters including 2 foreigners were killed and 10 others injured, the official said, adding they were deafeated.
"Even as large parts of our homeland have been freed from the enemy yet the foreign occupying forces continue exercising military and political influence in our Islamic country", the Taleban statement said.
When Senator Jeanne Shaheen asked Pompeo to ensure that the deal between the Taliban and the USA protects the rights of the Afghan women, Pompeo said, "Remember, the Afghans will ultimately decide".
Taliban forces attacked the northern Afghan city of Kunduz on Saturday, a day after the launch of their annual spring offensive, as fighting intensified across the country ahead of the next round of peace talks with US representatives. Referring to ongoing talks between the USA and the Taliban, the Kabul government urged pro-peace elements within the insurgents to shun violence and bloodshed.
Peace talks with the Taliban kicked off previous year, as US President Donald Trump vowed to reduce the number of US troops in Afghanistan.
According to Dawn news reports, Pompeo's remarks have come during a two-day congressional hearing on the U.S. state department's proposal of a budget this week.
The statement says that by announcing offensives, the Taliban has often targeted "innocent people in Afghanistan" while they have been dictated by "strangers" and that they have used civilian houses as a shield.
The insurgents effectively control almost half of Afghanistan and have continued to launch daily attacks on security forces despite holding several rounds of peace talks with the United States in recent months.
The spring offensive traditionally marks the start of the so-called fighting season, though in reality fighting in the last winter has continued unabated.
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". Several rounds of negotiations were conducted by the United States in Doha, Qatar's capital city.