Aides to Governor Deval Patrick have dropped an initiative for a new tax on “e-cigarettes” after gauging political appetite among lawmakers and finding it limited, legislative officials said.

Administration officials checked in recent weeks with members of the Legislature to find out whether lawmakers, who have shied from some of the tax hikes Patrick has previously proposed, would go along with a new levy on the devices, which offer a tobacco smoking-like experience. The administration was considering including the tax in the budget Patrick will unveil next week.

Massachusetts would have become the second state, after Minnesota, to impose a tobacco tax on e-cigarettes at a rate similar to traditional cigarettes, according to the National Council of State Legislatures.

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Reaction, the legislative officials said, was cool. Patrick’s budget proposal, set for a Jan. 22 roll-out will not include the e-cigarette levy, spokeswoman Bonnie McGilpin said.

The e-cigarettes are legal for minors to purchase in Massachusetts. A House billed, filed by Public Health Committee co-chair Representative Jeffrey Sánchez, Democrat of Jamaica Plain, would classify e-cigarettes as nicotine products and prohibit their sale to minors, but not tax the products.

The appeal to young people of the e-cigarettes’ comparatively low price point was a top argument for the new tax made by administration officials, said one person who had heard the pitch.

Before a meeting on Monday with Senate President Therese Murray and House Speaker Robert DeLeo, Patrick said he was planning to include in his budget the same set of tax proposals the Legislature has previously rejected, calling them “the same old ones we’ve proposed.” Those measures include removing candy and soda from the list of tax-exempt food products.

“Nothing new,” Patrick said.

Lawmakers last year slammed Patrick’s proposed $1.9 billion tax hike, which would have funded transportation projects and education programs. Instead, they opted for a $500 million tax boost and dedicated the revenues to transportation.

But legislators are frequently more accepting of “sin taxes” that can be framed as beneficial to public health. Last year, as part of the tax hikes, the Legislature approved a $1 per pack bump in cigarette taxes.

And the e-cigarettes represent a new market still developing, with policymakers scrambling to catch up, the way that laws surrounding cellphones and other comparatively recent technological advances are still taking shape.

Federal policymakers have yet to decide how to regulate the products nationally, said Karmen Hanson, health program manager at the NCSL.

Public health experts have been divided on the effects of e-cigarettes. The products do not emit smoke the way traditional cigarettes do, and do not contain tar. Cartridges inside the products discharge liquid that is converted into vapor.

The Food and Drug Administration does not regulate e-cigarettes the way they do traditional tobacco products. Product advocates and some health professionals say e-cigarettes can help with smoking cessation and might inflict less health damage than other nicotine products.