"We can not downplay any possibility and any version, but if you are investigating the killing, you are looking for a motive", he said.
Teodor Atanassov, the chief police officer of the northern town of Ruse, told reporters the man - who has not been identified - would be freed "very shortly".
A Romanian man has been released from police custody after facing questioning for 24 hours over the death of the TV reporter. Her body was found on Saturday.
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The interior minister Mladen Marinov and a spokeswoman for the town's chief prosecutor were scheduled to hold a press conference later Tuesday afternoon.
Authorities said she died from blows to the head and suffocation.
Police said she had been raped, beaten and suffocated, with her mobile phone, auto keys, glasses and some of her clothes all missing.
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Bulgarian national radio reports that a suspect has been arrested in connection with the slaying of Bulgarian television reporter Viktoria Marinova, whose body was found dumped after she highlighted possible government corruption.
Bulgarian officials emphasized that there was no evidence yet to connect Marinova's killing to her work.
In October 2017, Maltese journalist Daphne Caruana Galizia was killed by a auto bomb near her home, while in February this year Slovakian journalist Jan Kuciak and his fiancée Martina Kusnirova were shot dead. Marinova, 30, hosted a show last month featuring two investigative journalists who were detained for their work on suspected fraud involving European Union funds.
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Authorities are now saying, however, that the motive was likely sexual assault, not an attack on a journalist, although the investigation is ongoing. In a recent program, she interviewed a Bulgarian journalist and one from Rise Romania, who had been temporarily detained in Bulgaria last month while conducting an investigation into a suspected EU-funds fraud.
It is not known if the killing is linked to Ms Marinova's work at a local TV station, but Bulgaria is said to be the worst country in the European Union for press freedom.
"Shocked by the horrendous murder of Victoria Marinova. He has been charged in absence for two crimes - rape and premeditated murder with extreme cruelty", Tsatsarov said.
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"I have read monstrous things about Bulgaria in the past three days and nothing was true", Borissov said on Wednesday, charging that some "politicians are infatuated with sending emails to Brussels and the U.S., as if this is not something that happens in other countries". "Again a courageous journalist falls in the fight for truth and against corruption", he tweeted Sunday, not long after the news of the murder broke.