The regional leader of Ingushetia, Ruslan Aushev, signed the decree this week, based on a traditional Islamic practice permitting men to have four wives.
President Aushev, who has one wife, called for Russia's parliament to approve changes to Russian federal law to allow the move.
"The Ingush population has fallen sharply in recent years and polygamy could be a solution to this problem," he was quoted as saying.
He added that his decree was "pure pragmatism and the legalisation of the de facto situation".
The president's press secretary said many men already had two or three wives - but only the first one was registered under Russian law, which meant children were not protected and the other wives had no rights.
But Russian Justice Minister Pavel Krasheninnikov said on Wednesday the measure was unconstitutional and should be scrapped.
'A tragedy'
Mr Aushev said his decree only permitted polygamy in certain cases, for instance if a woman could not conceive.
"For an Ingush family, that is a real tragedy,'' said Mr Mr Aushev, adding that a man's life was wasted without a male heir.
The proposal to allow polygamy was popular among both men and women interviewed in the Ingush capital Nazran.
"If a man can support them, let him marry 10 times," one woman said.
An official at Nazran's marriage registration bureau said several men had already applied to register a second wife, but so far requests were being denied.
Bride stealing
Islam has been on the rise in the Caucasus region in recent years after being discouraged during the officially aetheist Soviet years.
In the breakaway region of Chechnya, at least one prominent local politician, Movladi Udugov, has two wives.
It is not the first time Ingushetia has come up against the authorities in Moscow.
Earlier this year, Mr Aushev tried to hold a referendum which would have legalised traditional Ingush customs, like the carrying of daggers and a ritual stealing of brides.
He backed down under heavy pressure from Moscow.
Correspondents say this is not just a dispute about folklore. Mr Aushev wants to steer his tiny republic on a middle course between outright secession, like the Chechens and complete loyalty to Moscow.
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