The dead included 47 law enforcement officers or officials, the ITAR-Tass news agency reported, citing Beslan Khamkoyev, acting interior minister of the republic of Ingushetia. A U.N. humanitarian worker was among the dead, authorities said.
Three high-ranking regional officials also were among the dead in the militants' foray into Ingushetia.
The attacks underscored the Russian military's failure to defeat separatists in neighboring Chechnya after five years of fighting, and raised new fears of spreading violence in southern Russia.
Many Chechen fighters trained and fought with the Taliban and al Qaeda in Afghanistan. Russia says many Arabs and other foreigners fight side-by-side with the Chechen rebels.
The Chechen militants also are said to receive support from al Qaeda and have strong contacts with the Wahhabi Muslim sect of Saudi Arabia, birthplace of al Qaeda chief Osama bin Laden. The deeply fundamental beliefs of Wahhabism are believed to be bin Laden's spiritual foundation.
Russian President Vladimir Putin ordered authorities "to find and destroy" the militants, whose raid came amid preparations for an August election to replace Kremlin-backed Chechen President Akhmad Kadyrov, killed last month in a bombing. Kadyrov's death was seen as a significant blow to Putin's efforts to bring some stability to Chechnya, devastated by two wars since the 1990s.
"Those who can be caught must be taken alive and brought to trial," Putin told a Kremlin meeting of police and security officials in remarks shown on state television.
Shortly before midnight Monday, about 100 fighters armed with grenades and rocket launchers seized the regional Interior Ministry in Nazran, the largest city in Ingushetia and attacked border guard posts there. They also attacked posts in the villages of Karabulak and Yandare, near the border with Chechnya, regional emergency officials said.
Interior Minister Rashid Nurgaliyev told Putin that 15 officers from the Ingush Interior Ministry's central building defended it for nearly six hours in a bid to keep rebels from entering the jail cells and freeing captives, Interfax reported.
Authorities sent in reinforcements shortly after dawn, with a long column of armored personnel carriers, trucks and troops moving into Nazran through the border village of Chermen in neighboring North Ossetia.
By midmorning, most of the militants had fled into forests on the border of Ingushetia and Chechnya, authorities said. Ingush President Murat Zyazikov told Interfax a large number of weapons and ammunition were missing from police depots.
Russian media reported only two militant deaths. An Associated Press reporter also saw the body of one militant near Yandare.
At least one group of retreating rebels was caught by police near the Chechen border, and a firefight ensued, said Yakhya Khadziyev, spokesman for Ingushetia's Interior Ministry.
In Makhachkala, the capital of Dagestan that borders Chechnya to the north and east, three militants were killed by Russian special forces after an hours-long firefight, regional authorities reported.
Maj. Gen. Ilya Shabalkin, spokesman for the Russian forces in Chechnya, blamed Chechen rebels for planning the attacks, but said the raids were carried out by fighters recruited from both Chechnya and Ingushetia.
"The attacks were clearly saber rattling, aimed to demonstrate the rebels' effectiveness to attract funding from foreign terrorist networks," he said, according to the Interfax-Military News Agency.
Russian TV broadcast image of smoke-charred and burning buildings and burned-out vehicles.
The United Nations office in Russia said humanitarian worker, Magomed Getagazov, was killed when caught in the crossfire while returning home from work in Nazran.
Chechnya's Interior Minister Alu Alkhanov told ITAR-Tass that he believed Shamil Basayev, a Chechen rebel commander blamed for some of the most audacious attacks, was behind the violence. The Kremlin backs Alkhanov in Chechnya's upcoming elections.
Chechnya's separatist President Aslan Maskhadov warned recently that insurgents were preparing to undertake new offensives.
Russia's NTV television showed footage of an encounter with some of the presumed attackers, wearing masks and speaking accented Russian, at a border crossing with North Ossetia. One of the attackers, carrying an automatic weapon, identified the group as "the Martyr's Brigade," NTV reported. The man added, "We have shot everyone here. Go and announce that."
Acting Ingush Interior Minister Abukar Kostoyev, the health minister and a deputy interior minister were killed in the fighting, officials said. ITAR-Tass said Nazran city prosecutor Mukharbek Buzurtanov and Nazran district prosecutor Bilan Oziyev were also killed.
Russian forces withdrew from Chechnya in 1996 after a devastating 20-month war against separatists that left the region with de facto independence. They returned in September 1999, after rebel incursions into a neighboring region and after deadly apartment-building bombings in Moscow and other cities were blamed on the militants.
Although Chechnya is a largely Muslim region in overwhelmingly Christian Russia, the first of Chechnya's two wars was an essentially secular conflict. After Russian troops pulled out when Chechen rebels fought them to a standstill, the separatists increasingly took on a specifically Islamic mantle.