(CNN) -- Michigan Gov. Rick Snyder vetoed legislation that would have allowed concealed pistol license holders who undergo additional training to carry concealed pistols in schools and other public places, his office said Tuesday in a statement.
Snyder rejected the bill because it did not provide an opportunity for public places -- such as schools, day care centers and hospitals -- to exempt themselves from the provision, the statement said.
At present, Michigan law does not prevent holders of concealed pistol licenses from carrying guns in these areas as long as they do so openly.
Snyder recommended that the bill be modified so that it would not permit the open carrying of weapons in these public areas, but would permit concealed carry for license holders who undergo additional training, his statement said. But even with this modification, he would still want property owners to be able to decide whether to allow concealed weapons on their premises, he said.
"These public venues need clear legal authority to ban firearms on their premises if they see fit to do so," he said.
Also Tuesday, Snyder signed two bills that streamline the process for handgun purchases and eliminate restrictions on interstate rifle and shotgun transactions.
The bill was approved Thursday by the Republican-controlled state Senate and House.
In a news release, Snyder's office said the governor "had committed to give the bill additional scrutiny" prior to Friday's school shootings in Connecticut "in an effort to ensure that public safety remains a priority."
But Speaker Jase Bolger, R-Marshall, said in a statement that the bill "would have had no impact on that tragedy" in Connecticut.
He said it was "unfortunate a compromise was not reached" and added, "It also is unfortunate that this veto does not make Michigan citizens safer in gun-free zones. Neither the governor's approval nor his veto will stop evil from preying on innocent people.
"With this veto, however, open-carry still exists in schools, churches and other public areas, and we know that criminals do not respect gun-free zones. For these reasons, we will continue to work with the governor to best protect our law-abiding citizens' Second Amendment rights, as well as the safety and security of all of our citizens."
At present, 21 states ban carrying a concealed weapon on a college campus, according to the National Conference of State Legislatures; 23 states leave the decision to ban or allow concealed weapons on campuses to individual colleges and universities.