ST. PAUL — Gov. Mark Dayton said Monday it would be “pointless” for him to veto a bill stripping the Minnesota Lottery’s ability to sell tickets online if the Legislature votes convincingly for the restriction.

Dayton said he hopes lawmakers at least give the lottery adequate time to end its Internet games and minimize breached contracts. The Senate voted overwhelmingly last week for an immediate online lottery prohibition. A House vote could come soon.

The Democratic governor didn’t commit to signing the bill, but said a lopsided House vote would make a veto futile. He could also let it become law without his signature.

Dayton, who has expressed concern that profit motive by lottery competitors could be driving the clampdown, said he asked House Speaker Paul Thissen to build in a grace period for the lottery. Dayton said the lottery has commitments to vendors and to players who have purchased tickets on a subscription basis for Powerball, Mega Millions and other drawings months into the future.

“Like many things in this session it’s being rushed through without the forethought it deserves,” Dayton said of the bill.

Thissen, DFL-Minneapolis, said he expects a bill restricting online lottery sales to get a vote before the session ends in a few weeks. Top lawmakers from both parties have signed onto the effort. Some have moral concerns over gambling. Others fear the setting makes the games more addictive and still more are upset that lottery officials launched the games without consulting legislators.

“Personally I don’t think we should have the lottery going online without at least having some discussions in the Legislature about the parameters we put around it,” Thissen said Monday. “Moving from paper gaming to online gaming is very different.”

Criticism intensified when the lottery moved its franchise scratch-off games online beginning in February. Players could access instant-play games from their homes or smartphones rather than buying them in a store.

Lottery director Ed Van Petten has stood behind the online games in testimony before lawmakers, saying they are helping the lottery adapt to the times. He said the electronic tickets make up a tiny part of the agency’s profits, which are split between environmental accounts and the state’s general treasury. He insists there are safeguards in place to prevent underage purchases and limit weekly spending.

The bill also halts the lottery’s move to allow ticket purchases directly from gas pumps, which it has done on a pilot-project basis. Some convenience store owners have balked at the offering because it gives customers one fewer reason to come into their stores to buy other goods. Dayton said that signals to him that it “is just further evidence that this is about protecting turf and profits.”

Still, Dayton said he is being realistic that lawmakers opposed to the online and gas-pump games are likely to prevail.

In his three-plus years as governor, Dayton has never had a veto trumped by a two-thirds vote or an override even attempted. He said in the telephone interview that he won’t put lawmakers in that position on this bill.

“Exercises in complete futility have never appealed to me. If the margin in the House is similar to the margin in the Senate, there’s nothing more to debate,” Dayton said.