TARRYTOWN, N.Y. (CBSNewYork) — A day after the Gov. Mario M. Cuomo Bridge was supposed to open both lanes to traffic, Gov. Andrew Cuomo announced there would be no clear date on when the new span would be fully open due to safety concerns about the old Tappan Zee Bridge.

However, the company that owns the old bridge released a statement on Sunday night clarifying the Tappan Zee’s condition and when the other side of the new bridge will open.

“The safety of the traveling public and our workforce is Tappan Zee Constructors top priority,” Terry Towle, president and project executive for Tapopan Zee Constructors. LLC said. “After careful evaluation, Tappan Zee Constructors has determined that the old Tappan Zee Bridge east anchor span is damaged but currently stable with certain key components highly stressed. This condition does not threaten the new, twin-span Governor Mario M. Cuomo Bridge, which is prepared and ready to receive traffic.

“While there remains a possibility of the old bridge east span failing, in the event it does, it will fall within a safety zone that does not affect vessel traffic or the structural integrity of the new eastbound bridge.

“With the completion of this initial assessment, we have recommended to the Thruway Authority that traffic can be shifted to the eastbound span of the Governor Mario M. Cuomo Bridge. As things now stand, the traffic switch has been scheduled for Tuesday evening, weather permitting.”

Over the weekend, the New York Thruway Authority said the dismantling of the old bridge had led to a potentially dangerous and unstable situation where part of the bridge could fall off, or the whole remaining structure could collapse.

“There’s a very remote possibility a piece could hit the new span,” Cuomo said on Sunday. “(They) don’t believe the piece could damage the new span, but it could hit.”

Cuomo held a grand opening ceremony Friday to open the new bridge. He reiterated that issues with the old bridge are no longer a problem the state of New York is responsible to fix.

“The state does not own the old Tappen Zee Bridge,” Cuomo said. “The contractor called Tappan Zee Constructors owns the old Tappan Zee Bridge, so it is not our bridge. We are not responsible for it. They are the ones deciding if they can put people on it, whether it’s structurally safe, and what to do about the old bridge.”

How and when the removal work on the old Tappan Zee will resume is unclear.

The U.S. Coast Guard said an inspection found that a span of the old bridge had become “destabilized and could fall.”

The north span opened last October, replacing the Tappan Zee.

The project has been surrounded by controversy since the governor named it after his late father and former New York governor, Mario Cuomo. The New York state Senate and Assembly have introduced bills to rename it the “Governor Mario M. Cuomo Tappan Zee Bridge,” and thousands of people signed a petition to keep the old name.