AUSTIN, Texas – The Texas Republicans moved the state electoral overhaul legislation closer to enactment on Sunday, putting aside fierce opposition from the Democrats to gain approval from key House and Senate committees after hearings over the marathon weekend.

The committee’s votes, held just days after a 30-day special session, stick to Governor Greg Abbott’s schedule for swift action against legislation he has identified as a priority for his administration. The Senate, which consists of 31 members, is expected to vote on its bill on Tuesday. The 150-strong house is likely to take up its own version of the measure this week.

The Democrats on both committees united against the bills and prepared for further fighting on the Senate and House floors. Beverly Powell, a Senator from the Fort Worth suburbs who voted against the bill on committee, said Senate Democrats were planning “many” changes during the plenary debate and could try to propose an alternative bill.

It took the Senate State Affairs Committee about 45 minutes Sunday afternoon to approve the bill, known as SB1, in a 6-to-3 party election after modifying the bill slightly with nine Republican amendments. “We feel good about the bill,” said Bryan Hughes, chairman of the Republican committee.

Previously, the committee met for nearly 15 hours, ending at around 1:30 a.m. on Sunday, and heard testimony from more than 200 witnesses, many of whom were against the law.

The House Committee hearings lasted even longer, ending around 7:30 a.m. on Sunday with a vote on the adoption of the bill after nearly 24 hours of debate and public comment. All nine Republicans on the committee supported the bill, while the five Democrats voted against.

Mr. Abbott, a Republican, has said that passing a new electoral law is one of his top priorities. He called the legislature into the special session that began Thursday after the Democrats blocked the law in late May with an 11-hour walkout from the Capitol denying Republicans the quorum.

Hundreds of Texans flocked to the Capitol over the weekend to watch the committee hearings on Republican-sponsored voting laws, part of a national effort by the party to place new restrictions on state electoral systems. Republicans say the restructuring is necessary to improve voter integrity, but opposition Democratic forces are fighting what they call an unprecedented campaign to suppress the vote.

“This is the largest coordinated attack on democracy in our lifetime, and perhaps in the lives of this country,” said Beto O’Rourke, a former US representative and presidential candidate who took and was a leading role for the Democrats in voting on the subject for the hearing in the Capitol.

But Mr. Hughes, the Republican chairman, opened the hearing on Saturday by stating that the law was intended to “create a better electoral process that is safe and accessible”.

House and Senate Democrats have vowed to do whatever it takes to kill the legislature a second time, but their options are limited. They have indicated that they are ready to take another bold step, such as another strike or possibly the more extreme step of fleeing the state.

Studies consistently place Texas at the top of the list of states making it harder to register and vote, which in part explains why the Democrats view the stakes as so high.

Voting laws would, among other things, prohibit 24-hour voting and drive-through polling sites, increase criminal penalties for election workers who violate regulations, limit support for voters, and expand the authority and autonomy of partisan election observers.

But two provisions from the previous session that the Democrats had vehemently opposed were removed: a restriction on the Sunday election and a proposal that would have made it easier to reject an election.

For the weekend hearings, Democrats and opposition to the bill had gathered witnesses from across the state to testify.

State Senator Borris Miles, a Houston Democrat, said two busloads of Witnesses and a caravan of 20 cars had traveled from his district. Both Mr. Miles and Lina Hidalgo, the executive director of Harris County, the state’s most populous district, told reporters that the Houston area’s bills would take a heavy toll by introducing electoral innovations like the 24-hour vote that was tabled , would be reduced in the 2020 election.

“We’re under attack,” said Mr. Miles.

After starting the poll late by spending hours on a bail revision bill, the House committee worked all night to hear many of the nearly 300 witnesses who had pledged to testify. Some who waited in the committee room after sunrise began to joke about the time, thanking Trent Ashby, chairman of the Republican House of Representatives, for not stopping his testimony.

“Good morning, Mr. Chair, thank you for staying,” said Hector Mendez, who represented the Texas College Democrats group. “Good luck at 6:30 am,” said another witness.

Although the Democrats were looking for more time to digest the bill, Ashby said he wanted to move on to a committee vote because of the “compressed nature” of the special session. Before voting on sending the measure to plenary, the committee also rejected eight Democratic amendments, including on party-level votes.

Texas follows several other Republican-controlled battlefield states that have radically revised their electoral laws and introduced new voting restrictions this year. Since January, at least 22 bills have been signed in 14 states that make voting difficult.