“This is the first step in finding a new home for Madison Square Garden and building a new Penn Station that is as great as New York and suitable for the 21st century,” said Christine C. Quinn, the City Council speaker. “This is an opportunity to reimagine and redevelop Penn Station as a world-class transportation destination.”

Ms. Quinn renewed her call for the creation of a commission to devise the plans.

Civic leaders and some developers have long sought to rebuild Penn Station, a cramped and crowded maze for the more than 500,000 people a day who traverse it. But doing so would be an enormously complicated, multibillion-dollar undertaking that has foiled officials in the past. And anything can happen in the next 10 years, including several elections for mayor and governor.

James L. Dolan, who controls the Garden, the Knicks and the Rangers, offered a low-key response to the news that barely acknowledged the 10-year deadline. Mr. Dolan expects to complete this fall a $968 million overhaul of the Garden, which has been closing in its off-seasons to accommodate the work.

“Madison Square Garden has operated at its current site for generations, and has been proud to bring New Yorkers some of the greatest and most iconic moments in sports and entertainment,” Mr. Dolan’s company said in a statement issued Wednesday afternoon. “We now look forward to the reopening of the arena in the fall of 2013.”

Mr. Dolan announced the latest renovation of the Garden in 2008, just after the last $14 billion effort to move the Garden and transform the train station collapsed amid a severe recession, insufficient financing, an absence of political leadership and overreaching by the developers selected for the job.