New York State’s corrections department agreed on Thursday to allow six men who had sued to be able to view Monday’s total solar eclipse to do so at the upstate prison where they are held, but the department stopped short of lifting a statewide prison lockdown during the eclipse.

The men, inmates at Woodbourne Correctional Facility in Sullivan County, filed a federal lawsuit last week arguing that the lockdown during the eclipse violated their constitutional right to practice their religion.

Though they come from varying religious backgrounds, the men all believe that the eclipse “is a religious event that they must witness and reflect on to observe their faiths,” according to court documents.

“This is a huge win for them — they are all ecstatic,” said Chris McArdle, one of the lawyers who represented the men. “Keeping our fingers crossed that it’s not cloudy or raining, they are going to be able to practice their sincerely held religious beliefs, which is the outcome we always wanted for them.”

A spokesman for the Department of Corrections and Community Supervision said in a statement that the lawsuit had come “to an appropriate resolution.”

Jeremy Zielinski, one of the men who filed the lawsuit, asked in January for permission to watch the eclipse from Woodbourne’s main yard. In his written request to prison officials, Mr. Zielinski, who is an atheist, said he believed eclipses were times to “celebrate science, reason and all things Atheism.”