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.
