Thousands of people had joined a demonstration called by the main opposition Chadema party last week over the legislation, which its leader Freeman Mbowe says contains only "cosmetic" changes.
But the government of President Samia Suluhu Hassan insists the reforms will improve governance and democracy in the East African country of about 65 million people.
Next year Tanzania is scheduled to hold its first presidential election since the death of authoritarian leader John Magufuli in 2021 led to his deputy Hassan taking the helm.
FILE - Tanzania's President Samia Suluhu Hassan walks during a visit at the Bogor palace in Bogor, West Java on January 25, 2024.
"The president has the good intention of improving multiparty democracy in Tanzania through reconciliation and reforms," said Jenista Mhagama, a minister of state in the president's office who presented the bills before parliament on Tuesday.
"The electoral reforms we discuss today are the outcome of recommended changes by a taskforce formed by different political stakeholders in Tanzania," she added.
Last Wednesday's demonstration in the main city of Dar es Salaam was the biggest since the government lifted a ban on opposition political rallies a year ago.
Mbowe, who has spent time in prison under both leaders, said the bills being debated do not address concerns over the last election in 2020, which Magufuli won by a landslide despite opposition claims of fraud.
The Chadema party has been campaigning for constitutional reforms and greater independence for the electoral commission to be included in the legislation.
Criticism of the proposals has been directed in particular at a measure that would allow Hassan to directly appoint five of the 10 members of the electoral commission.
"Our opinions and those of the political stakeholders have been ignored," Chadema secretary general John Mnyika said Tuesday.
He said on X, formerly Twitter, that the debate is set to run only until February 2 according to the parliamentary schedule.
"The simple interpretation is that they (the bills) are going to be passed without initiating amendments to the constitution."
Parliament is dominated by the ruling Chama Cha Mapinduzi (CCM) party which has 364 out of the 392 seats.
Hassan has sought to reverse some of the more hardline policies of her predecessor Magufuli, whose strongman tendencies earned him the nickname "Bulldozer."
A ban on opposition gatherings was overturned in January 2023.
Shortly afterwards, one of Tanzania's most prominent opposition leaders, Tundu Lissu, returned to the country after having spent most of the previous five years in exile.