ST. PAUL  — A plan aimed at helping prevent bullying in schools was narrowly approved by the Minnesota Senate on Thursday, with supporters saying it would give educators better tools to help students.

The bill would require school districts to track and investigate cases of bullying and require schools to better train staff and teachers on how to prevent it. If the legislation becomes law, it would replace a statute that requires school districts to have a bullying policy but lacks any details on what the policy should contain.

Advocates say the state’s current anti-bullying law, at 37 words long, is one of the weakest in the nation.

After nearly six hours of debate, the Senate passed the bill 36-to-31. It now goes to the House, which passed a similar measure last year. In a statement Thursday evening, Gov. Mark Dayton said he supports the stronger protections in the bill.

Bill supporters say the current law creates a patchwork of policies across the state and has failed to protect students.

But opponents say the bill would amount to an expensive and unfunded state mandate on local school districts. They are also concerned about the bill’s “presumption” that a school will notify the parent of a student involved in bullying incidents unless “notifying the parent is not in the best interest of the student.”

In a statement, Denise Specht, president of the state teachers union Education Minnesota, said the bill will give educators better tools to help students.

“The Minnesota Senate took a huge step today to address bullying in our schools,” she said.

“Teachers know students do better when they are in class, focused and learning. They can’t do that if they’re afraid to come to school.”

The bill is sponsored by Sen. Scott Dibble, DFL-Minneapolis.