Klaus Iohannis gave no reasons for his rejection of Sevil Shhaideh, put forward by the Social Democrats (PSD), but there was speculation that it was due to her Syrian husband's background.
"I have properly analysed the arguments for and against and I have decided not to accept this proposal," the president told reporters, calling on the PSD to "make another proposal".
Shhaideh, 52, who has only five months ministerial experience, is from Romania's small and long-established Turkish minority, but her Muslim faith is not thought to have been the problem.
Non-profit investigative journalism group the Rise Project said that he has several times expressed his support for Syrian President Bashar al-Assad and for Lebanese Shiite movement Hezbollah.
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Website HotNews cited unnamed sources as saying that the security services had "strongly cautioned" against Shhaideh's nomination because of the closeness of her husband and his two brothers to the Assad regime.
This might have made giving Shhaideh the necessary security clearances to be the NATO member's prime minister problematic.
The PSD had proposed the previously little-known Shhaideh after its thumping poll victory on December 11 when it won 45 percent of the vote, enough to form a majority coalition with its partners ALDE.
The leader of the PSD, Liviu Dragnea, had withdrawn his own bid to become prime minister because of a conviction that bars him from office.
Shhaideh's personal closeness to Dragnea -- he was a witness at her wedding -- has led to accusations that he will remain in charge behind the scenes.
"In our opinion the president is determined to set off a political crisis," Dragnea said. "If our conclusion is that it is in the country's interest to suspend Mr Iohannis, I won't hesitate."
However, Taranu said that any attempt by the PSD to remove the head of state was problematic because Iohannis is entitled to request a second proposal for premier.
The PSD's election triumph came barely a year since anger over a deadly nightclub fire that killed 64 people forced it from office.
But during the campaign Dragnea focused instead on the economy, vowing to boost salaries and pensions in the EU's second-poorest country.
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