"Bombing raids against Dudayev's strategic targets were carried out," Grachev said, according to a brief urgent report by Itar-Tass.
Grachev also said that unidentified aircraft flying over Chechnya would be shot down.
"All the aircraft spotted over the territory without identification signs, and which will not respond to calls, will be destroyed without warning," he said.
Grachev and two other top security officials left Moscow for the southern region neighboring Chechnya earlier on Monday.
Grachev, Interior Minister Viktor Yerin and Sergei Stepashin, head of the counterintelligence service, flew to Mozdok in North Ossetia for a tour of inspection of the Russian soldiers and military hardware being amassed around Chechnya's borders.
Russian soldiers at the frontier -- about 70 kilometers from the Chechen capital Grozny -- told Western reporters Monday they were under orders not to let anyone with Chechen papers leave, effectively sealing off the breakaway region.
No one was available at the special Russian government center dealing with Chechnya to confirm or deny the report. But a top Chechen army officer earlier denied Russian accusations that Chechnya was bringing in foreign mercenaries.
"No planes with militants have arrived in Grozny and could not arrive because all airports in Chechnya have been destroyed," the officer told Itar-Tass.
Moscow has given moral and financial support to Umar Avturkhanov's opposition Provisional Council fighting Chechen President Dzhokhar Dudayev, who unilaterally declared his homeland independent from Moscow in 1991.
But until now Moscow has denied any involvement in the fighting.
Last week Moscow threatened to impose a state of emergency on the region unless fighting stopped by Thursday. After the deadline passed, President Boris Yeltsin said he would not impose a state of emergency soon.
But the troops kept arriving.
On Monday, Grachev told Itar-Tass that unless Chechnya's warring sides began negotiating, he did "not rule out the declaration of a special form of government in Chechnya" -- a bureaucratic term for government under a state of emergency.
Force would only be used if peace-making proved futile, he said. Just in case, three military groups were assembling around Chechnya's perimeter, composed of Defense Ministry, Interior Ministry and special troops.
In Grozny, Dudayev said he was ready for talks with Russia but he would not negotiate with opposition groups which have been fighting his own forces.
"I always was and still remain in favor of negotiations on an equal basis with the Russian leadership at the corresponding level," Itar-Tass quoted Dudayev as saying.
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