The competition between Conrail management and the Transportation Department for the hearts and minds of Conrail's 35,000 unionized employes tightened a notch yesterday when both sides claimed credit for restoring deferred employe wages.

Federally owned Conrail said it had reached agreement with 10 of its 16 unions representing 23,000 employes to pay them industry wages retroactive to last July 1. Agreements are expected with the other unions, a source said.

The employes agreed in 1981 to three years of wages 12 percent below industry rates to help the railroad recover financially. Last year, its profit was $500.2 million. Last Friday, Transportation Secretary Elizabeth Hanford Dole announced plans to sell Conrail to Norfolk Southern Corp.

Conrail Chairman L. Stanley Crane opposes that and wants Conrail sold to the public through a stock offering.

In announcing the wage restorations yesterday, Crane praised employes for their aid in helping the railroad recover and said, "We believe it is time to recognize the employe sacrifices in a tangible fashion."

Within an hour of that announcement, a DOT spokesman released a letter, dated Jan. 28, to the Railway Labor Executives Association that promised that Dole "will ask the Conrail board of directors to implement the wage" restoration immediately after selecting a buyer.