Morar, 24, was refused entry into the country in December just days after publishing a story that claimed the presidential administration used a secret multimillion-dollar fund to finance parties during the State Duma elections.
Authorities later said she was denied entry because she was a threat to national security.
In an open letter published in Monday's issue of The New Times, publisher Irena Lesnevskaya asked Medvedev to give Morar a passport and "put an end to this lawlessness."
"This would really prove that [your promise to] fight legal nihilism and corruption are not just words," Lesnevskaya wrote.
Morar applied for Russian citizenship last July after graduating from Moscow State University, Lesnevskaya wrote. By law, authorities should have granted or rejected Morar's application by April, but there has been no official response, she wrote.
A Kremlin spokeswoman declined immediate comment.
Morar is one of more than two dozen journalists refused entry over the past eight years.
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