Said Chitour, who works for the BBC and the Washington Post among others, has been held "arbitrarily" since intelligence services arrested him at Algiers airport on June 5, RSF said.
He appeared before a judge who ordered him detained, but news of his arrest only emerged in early July.
"There are no grounds for keeping Chitour in pre-trial detention and doing so for more than a month is clearly excessive," the New York-based RSF said.
"RSF is also concerned about the conditions in which he is being held because he is diabetic."
It said he could face life imprisonment if convicted. Intelligence sources told AFP that Chitour, who had been under surveillance for several months, was accused of passing secret documents to foreign diplomats.
His lawyer, Khaled Bourayou, told AFP that no confidential document was listed in the case against Chitour, and he wondered how a journalist and fixer could have had access to such papers.
"All that Said acknowledges is that he had meetings with Western diplomats, like many journalists, where he gave his views on the political and economic situation of the country," he said.
The US-based Committee to Protect Journalists (CPJ) said last week that Chitour's arrest "appears to be an attempt to keep information about Algeria out of the international press".
"We call on Algerian authorities to release Chitour, drop all charges against him, and to cease harassing and threatening journalists for their work," CPJ's Robert Mahoney said.
RSF, which ranks Algeria 134rd out of 180 countries on its press freedom index, last month accused the country of "harassment" and "threats" used to pressure journalists.
In December, a British-Algerian journalist died while serving a two-year jail term for "offending" Algeria's president. Mohamed Tamalt's lawyer said he had lapsed into a coma after going on hunger strike.
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