In addition to the Erie Canalway Trail, there is a patchwork of existing multiuse trails in the Hudson Valley. So statewide, the project would entail the construction of 350 miles of new trail, which would fill in the gaps and create long new stretches. Where possible, state officials are relying on publicly owned land, such as rights of way controlled by the Metropolitan Transportation Authority, which is a state agency.

But one long segment in the Hudson Valley crosses private property, and the State Office of Parks, Recreation and Historic Preservation has already begun talks with the landowner. Options include purchasing the land outright or compensating the owner for allowing public access on a strip of his property.

“Fortunately, that stretch has only one owner whom we are working with,” said Rose Harvey, the state parks commissioner.

Mr. Cuomo has set aside about $200 million in his proposed budget for the state trail, and it is uncertain whether lawmakers will agree to spend that amount with so many other competing interests. But the Legislature has supported Mr. Cuomo’s campaign to rehabilitate the state park system in recent years, approving nearly $500 million so far to address a backlog of deferred maintenance and capital projects. Another $400 million in improvements are planned through 2020.