BOSTON — Democratic Massachusetts Secretary of State William Galvin and his Republican challenger Anthony Amore clashed Monday in a bitter debate.

The two split on many issues during the half-hour match on WGBH, including whether the state should adopt same-day voter registration, which allows residents to register to vote and cast a ballot on the same day.

Galvin said he supports legislation that would allow same-day voter registration. One of the top jobs of the secretary of state’s office is to oversee elections.

“I’ve advocated for it. I’ve come up with a very specific plan to put it together,” Galvin said.

Amore said he’s against the proposal — at least for now.

“I think it’s the future ... but I’m not convinced it could be done securely,” Amore said, adding “people need to feel confident that when they go in, their vote counts.”

Amore pointed to the case of three New Hampshire residents accused of voting in both New Hampshire and Massachusetts in the 2016 general election. He said Galvin’s office did not have the systems in place to alert Massachusetts officials and that stronger state voter ID laws could have raised flags.

Galvin said under existing law, voters can be asked for identification if there are concerns about their identity in Massachusetts.

The two also differed on a new system adopted by lawmakers and signed by Republican Gov. Charlie Baker earlier this year that will automatically update a person’s voter registration when that person notifies a state agency like the Registry of Motor Vehicles of a new address or other change in their status.

Amore said he was concerned about the new system.

“I spoke to town and city clerks and they told me that it’s going to create a burden for them with all of this information coming into their offices that they have to deal with,” Amore said, adding he’s not convinced that when an individual goes to the registry, they can prove they are a citizen.

Galvin said Amore is echoing a Republican playbook aimed at creating more hurdles for people wanting to vote.

“Republicans are into having fewer people vote,” Galvin said. “I’m into having more people vote.”

The two also traded more barbed broadsides during the debate.

Galvin chastised Amore, saying he failed to attend nearly all of the town meetings in Swampscott — his hometown — after being elected town meeting member.

Amore didn’t dispute the absences.

“A decade ago, I was town meeting member and I did miss the meetings. I had a family issue that prohibited it. I didn’t run for re-election,” Amore said.

Amore in turn faulted Galvin for not attending meetings of the Massachusetts Historical Commission, even though he is chair of the commission.

Amore also said Galvin was abusing state dollars by using a taxpayer-funded voter information booklet sent out to households to talk about his efforts to fight investment fraud and protect the addresses of domestic violence victims. The page references Galvin by name about a dozen times.

“That’s essentially an ad,” Amore said. “It’s at least unethical.”

Galvin said that page is included in the booklet whether he’s on the ballot or not.

The tense debate ended with Amore calling Galvin “a liar” and Galvin calling Amore “a faker.”

Galvin is seeking another four-year term in the office he’s held since 1995. Amore works as director of security at the Isabella Stewart Gardner Museum in Boston.

Election Day is Nov. 6.