Her pledge came on Wednesday during a programme at the Ganabhaban in Dhaka.
Hasina brought up the issue of thorough probe into the allegations after the UN, the US, Britain and the EU made calls for enquiry following Tuesday's city polls that were boycotted midway by the Bangladesh Nationalist Party (BNP) and candidates it endorsed, bdnews24.com reported.
The BNP cited gross fraud by the ruling party supporters to make sure their candidates won.
The prime minister said, "I will look into the incidents that have taken place. I will be able to find out who got how many votes after I get the results of the centres."
She claimed the elections were free and fair and drew attention to the low percentage of voter turnout, 43.9 percent, during the polling in three city corporations.
"Why would fewer votes be cast if there was rigging?" she asked.