Speaking at an event here, Hasina said the he Saudi government "will assist us in these projects", the Dhaka Tribune reported.
Hasina's Awami League party is considered as the secular party while her rival Khaleda Zia's Bangladesh Nationalist Party (BNP) is close to hardliners.
Her move to build hundreds of mosques is seen as an attempt to woo Islamist voters who have been traditionally voting for Zia's BNP and her ally Jamaat-e-Islami, according to experts.
The event was organised by Al-Hiyatul Ulya Lil-Zami'atil Qawmiya Bangladesh, the highest organisation of Dawra-e-Hadith of Qawmi madrasa, to honour the prime minister following her government's recognition of the Dawra-e-Hadith degree of the Qawmi madrasa system.
Thousands of students and teachers of Qawmi madrasas attended the rally.
At the rally, Qawmi leaders expressed their desire to see the prime minister in power for a third consecutive term.
"Since Sheikh Hasina has recognised (the top Qawmi madrasa degree) we want her to come to power again, so that she can fulfil the rest of our demands,” Qawmi leader Fazlul Karim said.
The speakers said "there is a change in Bangladesh now, and Qawmi leaders were not able to receive a prime minister before, with such warmth, because none had listened to their demands."
On September 18, parliament passed a bill to recognise the Dawra-e-Hadith degree as equivalent to a post-graduate degree in Islamic Studies and Arabic.