At least 39 people died and 45 were wounded in an assault on a Shiite mosque in Kabul, Afghan Interior Ministry spokesman Najib Danish said.
The attacker detonated his suicide vest in Imam Zaman mosque in the early evening, police said.
At least 20 people were killed and 10 were injured in an attack on a Sunni mosque in Ghor province, west of Kabul, Danish said.
Abdulhai Khatebi, Ghor provincial spokesman, said the attacker detonated his suicide vest during worship services in the late afternoon. The mosque is in the province's Doleena district.
The US State Department condemned the attacks in a statement Friday, as well as others that took place in Afghanistan earlier in the week.
"In the face of these senseless and cowardly acts, our commitment to Afghanistan is unwavering," said Heather Nauert, spokeswoman for the State Department. "The United States stands with the government and people of Afghanistan and will continue to support their efforts to achieve peace and security for their country."
The two attacks are the latest in the country, where Afghan and coalition forces have been squaring off for years with Islamic militants, including the Taliban and ISIS -- both Sunni movements.
Sectarian tensions have raged for some time between members of the Sunni and Shiite denominations of Islam. But there were no immediate claims of responsibility for Friday's attacks. ISIS has claimed responsibility this year for other attacks on Shiite mosques.
The violence comes a day after Taliban militants
stormed a base in Kandahar, in the south, and killed dozens of Afghan troops, the country's Defense Ministry said.
The ministry said 43 of the base's 60 troops died in the attack. A further nine were injured, six are missing and two were not harmed. Ten attackers were killed in the assault.
The Taliban claimed responsibility for that attack, according to a statement from the group's spokesman, Qhari Yosouf Ahmadi.
Taliban raids on Afghan military installations aren't uncommon. In April, a deadly raid on a northern army base left as many as 140 feared dead. That attack was revenge for the deaths of two Taliban officials in the region, a spokesman for the group told CNN.
On Tuesday, at least 41 people were killed and scores were injured in an attack on police headquarters in the Paktia provincial capital of Gardez, located in eastern Afghanistan.
Two car bombs exploded at the gate of the police headquarters, Danish said.
Afterward, five attackers entered the building and a five-hour gunfight ensued.