The demand came amid growing domestic opposition towards Romania's military involvement following the abduction of three journalists in March.
On Friday, the captors threatened to killed Prima TV reporter Marie Jeanne Ion, 32, cameraman Sorin Miscoci, 30, and Romania Libera newspaper journalist Ovidiu Ohanesian, 37, unless Romania removed its troops from Iraq within four days.
The opposition said troops should be withdrawn, but not under duress.
"We must find a correct balance to establish a calendar without giving the impression that we have yielded to political blackmail," former Foreign Minister Mircea Geoana, president of the ex-communist Social Democrat Party (PSD) told a news
Romania's government said it was in contact with the abductors but would not comment on the future of the 800 troops, sent to support the US-led invasion when Geoana's party was in power.
A pullout would be a blow to the US-led Coalition of the Willing, which has also seen Italy, Bulgaria, Poland, and Ukraine look at scaling down their presence in Iraq in recent months.
"We must find a correct balance to establish a calendar without giving the impression that we have yielded to political blackmail"
President of the Social Democrat Party (PSD)
On Sunday, an opinion poll said 70% of Romanians thought the new NATO member should withdraw troops from Iraq to save the journalists' lives, but Prime Minister Calin Tariceanu said the country would not rush to a decision.
About 1000 protesters joined the journalists' relatives and colleagues in a march in Bucharest on Monday holding aloft pictures of the hostages and banners declaring "freedom", but they stopped short of demanding a pullout.
"The authorities have tried to reassure us but we are very anxious because the deadline is so short," said Magdalena Ion, Marie Jeanne's mother. "But I'm sure it will be all right in the end."
Aljazeera broadcast a video on Friday, showing the three journalists sitting barefoot on a floor, apparently handcuffed, while masked men stood close by with guns.
The three were kidnapped in Baghdad on 28 March while on a short reporting trip.