In a statement in Nouakchott late on Wednesday, the lawyers said the court that tried the men was formed illegally, there were flaws in police reports, and that many of the accused had been tortured.
A total of 195 people, most from the military, went on trial late last year in the vast coup-prone former French colony which is hoping to get rich from offshore oil.
Four soldiers, including coup ringleader Salih Walad Hanina, were sentenced to life in prison with hard labour at the trial, which was held over 74 days at a military garrison east of the Islamic republic's capital Nouakchott.
"We have consequently decided ... to lodge an appeal so that the supreme court can rule on the serious infringements of the law noted during this trial and on this basis quash the sentences against the condemned," the statement said.
"The judges gave no response to the denunciation of serious torture exposed in detail by the majority of the accused who were victims," it added.
Hanina pleaded guilty to a June 2003 attempted putsch, during which he came close to toppling President Muawiya walad Sidi Ahmad Taya during two days of fierce street fighting in Nouakchott before loyalists regained control.
Mauritania's government says it has since foiled two more coup attempts in 2004 by dissidents linked to Hanina.
Critics say the two latest coup bids - for which the government has also blamed Burkina Faso and Libya - were a pretext to justify a clampdown on political opponents.
Haidalla was acquitted of charges
of funding the coup attempt
During the trial, three opposition politicians, including former military ruler Muhammad Khuna, were acquitted on charges of funding the coup attempts. The rest of the defendants were sentenced to between one and 15 years.
Hanina was removed from the army after being accused of stirring discontent over Mauritania's links with Israel.
The country is one of only three Arab League members to have full relations with Israel.
Taya, who first seized power in a coup in 1984, has angered many Arabs in a nation straddling black and Arab Africa by shifting support over the past decade from former Iraqi leader Saddam Hussein to Israel and the United States.