Friday, as they officially launched their spring offensive in a year that has already seen fierce fighting.
There were no casualties in either rocket attack, officials said.
This year's fighting season is expected to be intense after NATO forces ended their 13-year combat mission in December.
The Taliban claimed in an emailed statement to have launched 108 attacks across the country on Friday and to have "killed and wounded many Americans" at Bagram Air Base outside Kabul, the capital.
One rocket did land inside the sprawling Bagram base but caused no injuries, according the NATO-led coalition that continues to train and support Afghanistan's security forces.The Taliban have been fighting the Afghan government and its foreign backers since their hard-line Islamist government was ousted from power by U.S.-backed Afghan forces in 2001.
Also on Friday, several insurgent rockets landed in the capital of Ghazni province in central Afghanistan, said Mohammad Ali Ahmadi, deputy governor.
One rocket landed next to the building of the local women's affairs department, another inside the governor's compound and yet another hit a wall of a museum.
"Fortunately, they didn't cause any casualties or huge damage," Ahmadi said.
In the southern city of Kandahar, a bomb blast wounded three civilians, police said.
Insurgent fighters also attacked multiple police checkposts in the eastern provinces of Logar and Paktia. However, police chiefs of both provinces said by telephone that their forces repelled the attacks and suffered no casualties.
The Taliban typically announce a spring offensive to coincide with the melting of snow that usually intensifies fighting.
This year has already seen a surge in violence. Insurgents this month have already overrun several police and army posts in the northeast and killed eight people in an attack on a courthouse in the northern city of Mazar-i-Sharif.
Last year was the worst for civilians since the United Nations began keeping records in 2009, with more than 10,000 civilians killed or injured in the conflict in 2014.