Early Wednesday, the lower chamber of parliament examined over 100 proposals, including one that would reject all future requests to build nuclear plants. This one was accepted by 101 votes to 54.
The upper chamber will in turn meet on June 16 to discuss the issue.
A final decision will be made only "in a few months' time" through amendments of the legislation, a spokesman from the energy ministry said.
Any new draft legislation can also be put to the population for a vote through a referendum.
The Swiss government on May 25 recommended that nuclear plants be phased out. The move follows a decision to suspend plans to replace its nuclear power stations in the wake of the Fukushima accident in Japan in April.
The government predicted that a programmed exit from nuclear energy would favour businesses involved in green technology, boost employment and help Switzerland deal with expected rising electricity prices in Europe.
Initial calculations estimate that the cost of reshaping the country's energy resources, offset by measures to cut consumption, would amount to between 0.4 percent and 0.7 percent of gross domestic product.