GENEVA — Despite arm-twisting and vocal opposition from nuclear powers like the United States, six non-nuclear countries urged the U.N. General Assembly Wednesday to work toward a “legally-binding” accord to ban nuclear weapons in hopes of ridding them from the planet altogether one day.

The countries — Austria, Brazil, Ireland, Mexico, Nigeria and South Africa — sent world diplomats a draft text that calls for a U.N. conference next year to draw up a treaty banning nuclear weapons, diplomats said. The Associated Press obtained a copy of the text, which is to be considered at the U.N. in New York starting next month.

The 3-page draft, which heads to a U.N. committee in New York, hews closely to a resolution passed at a working-group meeting of non-nuclear states in Geneva last month. The text urges states “to negotiate a legally-binding instrument to prohibit nuclear weapons” that would aim one day for their “total elimination.”

It also says a U.N. conference should convene next year for 20 working days in two sessions, bringing international organizations and civil society into the process of drawing up a treaty.

However, it stops short of setting a calendar or deadline for an eventual passage of the treaty.

The text also urges countries to apply working group recommendations to increase transparency about the risks of nuclear weapons, enact measures to reduce the risk of accidental or unauthorized detonations, and raise awareness about the consequences of a detonation.

Austria’s permanent representative in Geneva, Thomas Hajnoczi, called the text a “big step.” While acknowledging that security agreement at the U.N. for a nuclear weapons ban would likely be a long process, Hajnoczi expects a vote on the text by a U.N. committee on disarmament around Nov. 1 that could send it to the assembly in December.

“It’s hard to see how this treaty wouldn’t strengthen the non-proliferation regime,” he said, alluding to the Nuclear Non-Proliferation Treaty that has been a global benchmark of limiting nuclear weapons for years.

But only a day earlier, Anita E. Friedt, a top State Department official on arms control, told a Center for Strategic International Studies panel in Washington that the United States believes “pursuit of such a ban is unrealistic and simply impractical” and “could actually end up harming” broader, tangible efforts toward disarmament.

Another Geneva diplomat familiar with the text, speaking on condition of anonymity amid concern about reprisals, said the refusal of nuclear-armed countries to take part in the working group actually encouraged some states to support work toward a ban, because it suggested to them that the powers weren’t taking disarmament seriously enough.

The drafters and other countries favorable to a ban had come under “incredible” pressure not to move forward, the diplomat said. The “arm-twisting” involved constant calls, diplomatic “demarche” insistence, and even a “division of labor” among key nuclear powers to focus on specific regional governments to lobby against the initiative, the diplomat said.

Nuclear-armed France, for example, was to focus on African countries, and Britain was to concentrate on potential ban supporters in Europe along with the United States, which was to lobby countries in NATO and others covered by the U.S. nuclear “umbrella,” the diplomat said.

U.S. President Barack Obama has expressed a long-term commitment to pursuing a world without nuclear weapons. Defense Secretary Ash Carter in London recently acknowledged the inherent risk of nuclear arms. Carter said, “We’re going to have nuclear weapons as far into the future as I can see,” and that they need to be safe, reliable and secure.

Austria’s Hajnoczi acknowledged it was tough to know what nuclear-armed states including China, Russia, France, Britain and the United States might do to thwart the march toward a treaty.

“We will see what those countries who do not like the project will do….That is something we cannot predict,” he said.

This story has been corrected to show that the draft sent to world diplomats calls for the U.N. General Assembly to launch work on a nuclear weapons treaty, not the treaty itself.