The armed group launched a pre-dawn attack on an army base in northern Kunduz on Tuesday, killing 26 members of the security forces, Mohammad Yusouf Ayubi, head of the provincial council said.
There were at least 23 soldiers and three members of the local police force among those slain.
According to Ayubi, 12 troops were wounded in the Taliban onslaught, which lasted for over two hours until reinforcements arrived at the besieged base and the attackers were repelled.
"Day by day, the security situation is getting worse in and around Kunduz city," said Ayubi, adding there are fears the city could again fall into the hands of the Taliban as it did briefly on two occasions in recent years - in September 2015 and in October 2016.
In the northern Baghlan province, at least 11 policemen were killed when fighters stormed a checkpoint, provincial officials said on Tuesday.
The attacks were reported as Taliban representatives began meetings with prominent Afghan figures, including former President Hamid Karzai, opposition leaders and tribal elders, but not Kabul government officials.
In the checkpoint attack, the Taliban targeted the local police force in the province's Baghlani Markazi district on Monday night, triggering a gunfight that lasted for almost two hours, said Safder Mohsini, head of the provincial council.
Five policemen were also wounded and the Taliban seized all the weapons and ammunition from the checkpoint before reinforcements arrived, he said.
"They arrived there late, fought back and managed to get the checkpoint under control," he added.
Earlier on Monday, the Taliban targeted a local pro-government militia in a village in northern Samangan province, killing 10 people, including a woman, said Sediq Azizi, spokesman for the provincial governor.
Four people were also wounded in that attack, in Samangan's Dara-I Suf district, he said.
According to Azizi, the Taliban targeted local villagers, including women and children. As the area is very remote, the villagers have their own militia to provide security for their area and defend their homes from armed fighters.
The Taliban claimed both attacks in statements to the media.
They have been staging near-daily attacks and inflicting heavy casualties on the embattled Afghan army and security forces, as the United States is eager to pull out of the war-torn country.
The two-day meeting in Russia's capital between the Taliban and mainly Afghan opposition figures is seen as another step in a process aimed at resolving the country's 17-year war, one that has escalated since the appointment of US peace envoy Zalmay Khalilzad last September.
Ghani has repeatedly called on the Taliban to begin talks with his government, which the Taliban refuses to recognise, calling it a "puppet" of the US.
He was excluded from six days of discussions between the armed group and the US in the Qatari capital, Doha, last month that reportedly sealed the outline of a peace deal.
Abdullah Abdullah, the country's chief executive, said on Monday that the Afghan government should be at the centre of any peace talks, adding that Kabul "would prefer the Moscow meeting had a different shape".
Abdullah said that the Taliban was the biggest obstacle to peace, but that if the Moscow meeting creates "an opening for real peace talks, it would still be a step forward".
Among those attending the meeting is Haneef Atmar, a former national security adviser who is running against Ghani in presidential elections set for July. Former Governor Atta Muhammad Noor and former Afghan President Hamid Karzai, both Ghani's rivals, are also attending.
The Taliban is scheduled to hold another round of peace talks with the US in Doha on February 25.
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