Massachusetts Senate leaders Friday unveiled a modest rewrite of the voter-approved marijuana legalization measure, setting up a pivotal showdown with the House of Representatives that will dictate how pot is grown and sold in the state.

Earlier this week, House leaders revealed a bill that would significantly change the ballot law, increasing pot taxes to 28 percent from 12 percent. Amid sharp criticism from advocates, the public, and other lawmakers, the proposal was quickly withdrawn from a scheduled vote.

The Senate bill would leave in place the initiative’s lower pot tax rate, and it would maintain a requirement that only voters — not municipal officials, as House leaders proposed — can ban pot shops in their city or town.

Overall, Senate officials said, they intend to more closely hew to the ballot question passed by 1.8 million Massachusetts voters in November.

“We are not starting from scratch. We are starting from a law that was passed by the voters,’’ Senator Patricia D. Jehlen said. “And we need to justify any amendments that we make to it.’’

The bill, according to Jehlen and a two-page outline of the legislation, would make some changes to terms approved by voters.

Like the House plan, it would rob Treasurer Deborah B. Goldberg of her unilateral oversight of the cannabis industry. The governor and attorney general would also get to appoint some of the commissioners who will write regulations on everything from neon signs in pot shop windows to the warning labels on marijuana-infused cookies.

And, like the House bill, the Senate plan would merge oversight of the recreational and medical cannabis markets.

Both proposals would also create a commission to study how law enforcement can detect drivers who are high on marijuana.

But there are differences between the bills, including a provision in the Senate version that would clarify that people charged with certain marijuana crimes in the past can seal their criminal records.

The House bill had no such “expungement’’ provision, which prompted concern from members of the Massachusetts Black and Latino Legislative Caucus. Advocates have long argued that the country’s “war on drugs’’ disproportionately swept up people of color. Now that marijuana is legal, they want to ensure people in those communities who have long-ago drug charges aren’t frozen out of the industry.

Jehlen suggested the House had erred by including too many specifics in its bill, including the exact wording of warning labels for edible marijuana products. Other states with recreational shops have had to adjust such rules as the dynamic industry evolved, she argued. That’s a process better suited to a responsive regulatory body, she said, than the slower-moving Legislature.

The Senate bill, “it’s not as prescriptive,’’ Jehlen said. The bill text has not yet been made public, and Jehlen said Senate lawyers were still perfecting its details Friday afternoon.

Jehlen’s plan, like the House proposal, would leave some fundamental aspects of the ballot question in place. Growing, buying, possessing, and using limited quantities of marijuana by adults 21 and older would remain legal. And both foresee retail pot stores still opening in July 2018.

On Wednesday, Speaker Robert A. DeLeo abruptly pulled the House’s pot proposal, which drew denunciation from a wide range of critics. House lawmakers plan to vote on a revised version of that bill out of the Legislature’s marijuana committee Monday. A vote by the full House is expected later next week.

Jehlen, the Senate chairwoman of the Legislature’s marijuana committee, argued that the 28 percent tax rate proposed by the House was too high and would undermine a robust legal market.

Noting that consumers regularly shop in New Hampshire to avoid Massachusetts’ 6.25 percent sales tax, Jehlen said cannabis users will inevitably seek out the cheapest pot — even if that means buying it on the black market or from a dispensary in Maine, where the pot tax is set at 10 percent.

“The price differential matters,’’ she told reporters gathered in the office of Senate President Stanley C. Rosenberg. “Many people prefer a regulated product, but if the price differential is 28 percent — think about what the people you know would do. You think they’ll walk past their neighborhood dealer they’ve been buying from for years?’’

The delay by the House this week has raised questions about whether lawmakers will meet their self-imposed June 30 deadline to get a bill to Governor Charlie Baker’s desk.

Joshua Miller can be reached at joshua.miller@globe.com. Dan Adams can be reached at daniel.adams@globe.com.