In one attack, a suicide bomber targeted worshippers in a Shia mosque in Kabul, police said on Friday.
A man "entered the mosque in Police District 13 of Kabul city ... [and targeted] worshippers," General Mohammad Salim Almas, Kabul crime branch chief, told AFP news agency, describing the attacker as a suicide bomber.
Major-General Alimast Momand, of Afghanistan's interior ministry, told the Associated Press news agency that the suicide bombing at the Imam Zaman Mosque in the city's Dashti Barch area killed at least 30 people and wounded 45 more.
He said the attacker was on foot and walked into to the mosque where he detonated his explosives.
Najib Danish, an interior ministry spokesman, said "39 people have been killed and 45 injured in the Kabul mosque attack", but the numbers could not be independently confirmed.
The Islamic State of Iraq and the Levant (ISIL) group said in the statement that a suicide bomber had detonated a vest but did not provide evidence to support its claim.
An Afghan government official told Reuters news agency that security forces at the scene had removed at least 30 bodies.
Reports said the victims were members of the minority Hazara Shia community.
Mohammad Sabir Nassib, head of the local Isteqlal Hospital, said it received the bodies of two people slain in the attack as well as two wounded.
Friday's second attack during prayers occurred at a Sunni mosque in the central province of Ghor.
Mohammad Iqbal Nezami, a spokesman for the provincial police, said at least 33 people were killed in the bombing that appeared to target a local commander.
Initial reports had 10 dead in that attack.
The target was Abdul Ahed, a former militia commander and Jamiat party leader who had sided with the government.
He was killed along with as many as 30 other worshippers, according to a statement from Atta Mohammad Noor, a leading figure in Jamiat and the governor of Balkh province.
Among the dead were seven of Abdul Ahed's bodyguards.
Later on Friday, the Afghan president issued a statement condemning the two mosque attacks.
Ashraf Ghani said the incidents showed that "the terrorists have once again staged bloody attacks, but they will not achieve their evil purposes and sow discord among the Afghans".
Al Jazeera's Jennifer Glasse, reporting from Kabul, said: "We have no idea who carried out the attack tonight in Kabul, but across Afghanistan this week, we have seen more than 130 people killed - in the north, in the south, in the southwest, in the east - mainly security forces killed by the Taliban."
She said Taliban fighters are escalating their attacks on security forces, "trying to show the government they have some power here, trying to put pressure on a government that is trying to pressure them to come to the peace table".
Afghanistan's Shia population has been heavily hit this year, with at least 84 people killed and 194 wounded in attacks on Shia mosques and religious ceremonies, according to a UN report released last week.
Among those were at least two attacks on mosques in Kabul in August and September.
The last attack in Kabul happened on September 29 as the faithful prepared to commemorate Ashoura, one of the holiest days in the Islamic calendar.