* Prosecutors order probe of Mursi's political rivals
* Opposition calls it a scare tactic
* Scant sign of consensus Mursi needs to repair economy
By Tom Perry and Yasmine Saleh
CAIRO, Dec 28 (Reuters) - Egypt's opposition accused President Mohamed Mursi's Islamist allies of trying to muzzle dissent on Friday after prosecutors decided to investigate whether prominent government critics were guilty of sedition.
The probe, which comes a month after Mursi replaced the chief prosecutor, further sours the political climate as the leader and his opponents face off over a new constitution that became law on Wednesday.
Critics of the new charter say it uses vague language, fails to enshrine the rights of women and minorities and does little to champion the rights of Egyptians who rose up last year to overthrow army-backed strongman Hosni Mubarak.
Supporters say it protects personal rights that were often trampled upon during the Mubarak era and a subsequent spell of army rule.
The constitution text won about 64 percent approval in a two-stage referendum but Mursi's opponents vowed to continue protests and rejected his calls for a national dialogue.
Prosecutors ordered the inquiry into three of the president's most prominent opponents on Thursday - former Arab League chief Amr Moussa, Nobel Peace Prize laureate Mohamed ElBaradei and leftist Hamdeen Sabahy.
Moussa and Sabahy both challenged Mursi for the presidency in a June election which followed the 2011 uprising.
The prosecutor's office said the three had been accused of inciting supporters to rise up and overthrow Mursi, the country's first fairly elected leader.
Mursi's critics saw an attempt to intimidate them into silence and vowed to continue challenging his rule.
"I believe this is orchestrated by the Brotherhood leadership," Hussein Abdel Ghani, a spokesman for the country's main opposition umbrella group, told Reuters. "The Mubarak regime used to order the same tactics."
"But we are going to use our full rights, our civil tactics, to demonstrate our opposition to this regime," he said.
The charged atmosphere makes it harder for Mursi to bolster his authority and muster a consensus for unpopular austerity measures vital to preventing a weak economy from collapsing.
Mursi is hoping that the quick adoption of the constitution and holding elections to a permanent new parliament soon will help end the long period of turmoil since Mubarak's overthrow in February 2011 that has wrecked the economy.
But the Egyptian pound tumbled to its weakest in almost eight years this week after the constitution was approved. People unnerved by the continued political tension rushed to hoard dollars and gold.
The government ordered new restrictions on foreign currency apparently designed to prevent capital flight. Leaving or entering with more than $10,000 cash is now banned.
Mursi was propelled into office thanks to the rallying power of his Muslim Brotherhood, the country's main opposition group under Mubarak that was banned from formal politics for decades.
Ahmed Sobeih, a spokesman for the Brotherhood's Freedom and Justice Party, dismissed Abdel Ghani's accusation of an organised legal campaign against Mursi's opponents.
"We must get away from the language of mutual accusations," he said, adding that "dozens" of similar complaints had been filed against Brotherhood leaders.
Mursi appointed Chief Public Prosecutor Talaat Ibrahim when he assumed sweeping new powers on Nov. 22. Ibrahim's predecessor, Abdel Maguid Mahmoud, had served for many years under Mubarak.
Judicial sources said the inquiry against Moussa, ElBaradei and Sabahy followed a complaint from lawyers sympathetic to Mursi.
The trio are part of the National Salvation Front, an alliance of political groups that has spearheaded street protests against the government.
"The mere referral of these complaints to an investigative judge and the accompanying public announcement is already cause enough for serious concern," said Heba Morayef, Egypt director at New York-based Human Rights Watch.
A spokesman for Moussa said the accusations against him were groundless.
"What we read in the papers are several allegations that we have denied over and over in the past few months," said Ahmed Kamel, a spokesman for Moussa's Congress Party. "They are completely unfounded and have no relation to reality."