Governor Paterson is asking the Port Authority of New York and New Jersey for a comprehensive assessment of schedules and budgets for construction at the World Trade Center site.

The request for the assessment yesterday came just hours after the Port Authority acknowledged that it would hand over the site where Tower 2 is set to rise along Church Street at least one month late. The delay could cost the Port Authority more than $10 million in penalties.

“The rebuilding of the World Trade Center site must encompass clear and achievable timelines and budget goals that must be met at every step of the way. Furthermore, the stakeholders and the public must be kept up to date on progress in meeting the timetables and budgets as we move forward,” Mr. Paterson wrote in a letter to the director of the Port Authority, Christopher Ward.

In a statement issued yesterday, the Port Authority said it would live up to its agreement and pay the site’s developer, Silverstein Properties, $300,000 a day, beginning July 1, until it turns over the fully completed Tower 2 bathtub. The authority said it does not expect the site to be finished before August.

Last month, the Port Authority gave Silverstein Properties extensions for the completion of towers 3 and 4 to allow developer Larry Silverstein more time to negotiate with Merrill Lynch, which is negotiating with Mr. Silverstein as a possible anchor tenant.

“Everyone at Silverstein Properties is eager to start select work in July and looking forward to expanding over the entire Tower 2 site later this summer,” the president of World Trade Center Properties, Janno Lieber, said in a statement.