Afghanistan's Defense Ministry said on Sunday that the security forces had conducted 13 ground offensives and 12 aerial attacks in nine provinces, adding that 51 "terrorists" had been killed, 13 wounded and six arrested.
Local officials in the northern province of Balkh said at least three women and four children were killed in the air strikes, Presstv Reported.
The government said it would send a fact-finding mission to investigate the reports of civilian deaths, which had prompted protests in front of the provincial governor's office.
Over the last week, there were reports of Taliban attacks on government installations in different parts of Afghanistan.
The Taliban also said they had staged two more attacks against security forces over the weekend.
Taliban spokesman Zabiullah Mujahid said in a statement that Afghan security forces' checkpoints in Kunduz were attacked on Saturday night.
At least 10 members of the security forces were killed and three wounded in the assault, he added.
Taliban militants also captured a large weapons cache, the spokesman noted.
In a separate statement, the Taliban said its militants had ambushed an Afghan forces patrol in Balkh, killing eight security personnel.
The United States invaded Afghanistan in October 2001 and overthrew a Taliban regime in power at the time. But US forces have remained bogged down there through the presidencies of George W. Bush, Barack Obama, and now Donald Trump.
Some 19 years on, Washington is seeking a truce with the militants, who now control or have influence in about half of Afghanistan’s territory. The Taliban have rejected calls for a ceasefire and instead stepped up operations across the country over the past few months.
The Taliban have been negotiating with the Trump administration for more than a year over the withdrawal of US troops in exchange for security guarantees from the militants.
Negotiations began last year in the Qatari capital Doha, but have been interrupted at least twice after Taliban attacks on US military personnel in September and December.
Last week, another round of talks kicked off with US Special Representative on Afghanistan Zalmay Khalilzad meeting repeatedly with the Taliban's chief negotiator Mullah Abdul Ghani Baradar.
US and Taliban negotiators in Doha have reportedly taken a two-day break for consultations about how to overcome the recent hurdles in the talks.
In bilateral talks, which had excluded the Afghan government, US forces withdrawal from Afghanistan had been the main Taliban demand.
Nearly 20,000 US-led foreign troops, most of them Americans, are currently deployed in Afghanistan as part of a so-called mission to purportedly train, assist, and advise Afghan security forces.