Sissel Andersen and Steinar Bergstøl Andersen are calling for the southern town of Kristiansand to implement the drastic measure as a matter of urgency, broadcaster NRK reports.
The pair claimed the strategy had already worked in the Lithuanian capital, Vilnius, and asked the local branch of the party to adopt the measure as official policy.
“Rather than criminalizing beggars, I think we should perform a 180-degreee turn and criminalize people who give them money,” said Bergstøl Andersen in a statement.
“I would consider a fine of 4,500 kroner ($785), like they have in Vilnius, to be satisfactory.”
The pair urged people wishing to help beggars to instead donate money and clothing to specialist organizations.
Earlier this year, two Progress Party politicians from Tromsø in northern Norway sought to ban public begging, citing concerns that their town risked becoming too like the capital Oslo.
“We’re afraid Tromsø’s going to become a mini-Oslo, with floods of beggars, asylum seekers and street prostitutes,” Kristoffer Kanestrøm and Bjørn-Gunnar Jørgensen told newspaper Nordlys.