The proposals were brought forward in the wake of last November's Paris terrorist attacks.
A meeting on Tuesday of Parliament's internal market and consumer protection (IMCO) committee debated a raft of "compromise" proposals put forward by UK Tory MEP Vicky Ford.
Her proposals, which were generally welcomed by committee members, are designed to pave the way for formal negotiations to start on the draft legislation between Parliament, the Commission and member states.
Before that, the committee will vote next month on the compromise package.
Over 900 amendments to the Commission text have been put forward, including 800 from the IMCO committee.
The meeting started with members holding a minute's silence for the victims of the Orlando massacre at the weekend.
The Commission proposals, a revision of the EU firearms directive, are partly designed to stem the flow of illegal weapons to terrorist groups like I.S. as well as dangerous criminals.
However, several committee members criticised the draft as "unworkable", partly because they said it might also unfairly impact on people who own firearms legally, such as sportsmen and those in the hunting community.
French EPP group deputy Philippe Juvin said, "Hunters and shooters are not terrorists. They don't commit terrorist acts and we shouldn't be making life more difficult for these people. What we should be doing is terrorising the terrorists."
His comments were echoed by Maltese EPP group member Roberta Metsola, who said that despite the "global phenomenon" of terrorism, Parliament had to avoid a "knee-jerk" reaction to recent terrorist atrocities.
"We have to ensure that people like shooters and hunters do not become targets themselves," she told the committee.
Anna Maria Corazza Bildt, EPP group shadow rapporteur on the firearms dossier, agreed that while there was a need to "modernise" current gun laws, it was also important not to add "additional administrative burdens" on legal firearms holders.
Italian Socialist group member Sergio Cofferati also believed it was "crucial" to have medical checks on people seeking to own a firearm in order to ensure "they do not end up in the wrong hands."
Dita Charanzová, an ALDE group member from the Czech Republic, described the Commission proposals as "far from perfect", partly as she fears it may result in "massive" restrictions, particularly in ownership of semi-automatic weapons.
She said, "In finalising our position we need to strike the right balance between security concerns and the rights of gun owners."
Further comment came from Pascal Durand, a French Greens/EFA group deputy, who said the file was "one of the most sensitive" in the current parliamentary term.
He branded the commission proposals to update firearms legislation as "inadequate", saying there was also a need to make "efficient checks" on long-distance firearms sales.
A representative of the Dutch EU Council presidency told the meeting that he believes the agreement brokered last Friday with member states represented a "balanced approach" and called on Parliament to adopt its position on the draft law.
The aim, he said, was to start a formal dialogue once the Slovakian EU Council presidency gets under way on 1 July.
Ford brought the debate to a close by emphasising that the overall aim was to "close loopholes" in existing firearms legislation.
She is suggesting that a firearm should only be considered deactivated if the process is truly irreversible. She said there needs to be better exchange of information between member states and a reworking of the Commission's "impractical" plan to ban semi-automatic firearms that resemble automatic firearms.
She said, "The first text from the Commission was poorly worded and we need to make sure that the legislation is practicable."