In Parwan province, north of the capital Kabul, an election rally where President Ashraf Ghani was due to speak was attacked, and 26 people died.
Another blast, near the US embassy in central Kabul, killed 22 people.
The Taliban said they were behind both attacks. The group has continued a concerted bombing campaign while at the same time taking part in peace talks.
But US President Donald Trump described the negotiations with the Taliban as "dead" earlier this month.
The Taliban refuse to talk to the Afghan government and have vowed to disrupt the presidential election in the country on 28 September.
In a statement, they said: "We already warned people not to attend election rallies, if they suffer any losses that is their own responsibility."
Forty-two people are reported to have been injured in the election rally blast in Charikar, the capital of Parwan province, at 11:40 local time (07:10 GMT).
Children were among the casualties, medical staff said. The bomber, on a motorbike, triggered the blast at a checkpoint at the venue.
President Ghani, who hopes for a second five-year term, was not hurt.
Another suicide bomber targeted Kabul's busy Massood Square, the site of government ministries and Nato compounds, at 13:00 local time.
An additional 38 people were injured there, according to the Ministry of Interior Affairs.
On Twitter, the president called the perpetrator "a cowardly enemy".