The proposal would put heavy-smoking Japan in line with other developed countries, which nearly all impose heftier taxes on cigarettes and more tightly restrict public smoking.
The non-partisan parliamentary group headed by senior ruling party member Hidenao Nakagawa called for the price of a pack to rise to up to 1,000 yen (9.6 dollars) from around 300 yen now.
The proposal "aims to safeguard health," Nakagawa said in a written response to AFP.
"I also think Japan's tobacco tax is too cheap compared with the average in the world and in Western countries," he said.
Nakagawa -- who himself smokes two to three packs a day -- said the money from the hike would go to improve social security programmes.
He denied media reports that the proposal was aimed at allowing the government to avoid the politically sensitive step of raising the consumption tax to tame a ballooning public debt.
Economic and Fiscal Minister Hiroko Ota left open the possibility of raising the tax on cigarettes.
"The tobacco tax is of course one option" to raise taxes, she told reporters.
But she added: "We need to discuss the issue as part of an overall debate on reforming the tax system."
The news caused a sharp drop in share prices of Japan Tobacco, which enjoys a virtual monopoly on domestic sales and has been rapidly expanding overseas.
Its shares tumbled 29,000 yen or 5.64 percent to 485,000 yen, even though the market's benchmark index rose more than one percent to a five-month high.
Barclays Capital's chief Japan economist Kyohei Morita cast doubt on the cigarette proposal, saying that the rise would be so sharp that it would inevitably lead to decreased public consumption of other taxable items.
"In our view, the impact on the economy cannot be ignored, so 1,000 yen for a pack of cigarettes, while it might become a slogan, is unlikely to be realised," he wrote in a research note.