A Russian diplomat said there were no Russian casualties in the assault on the embassy. Political attache Andrey Avdeev added that there was no serious damage to the embassy.
There was no immediate claim of responsibility for the attack, but police confirmed reports that a document found on the dead attacker said it was a protest of Russia's military offensive against Muslim rebels in Chechnya.
Lebanese Muslim militants opposed to the military campaign in the Caucasus have staged protests against Moscow and have been raising money for the Chechens.
An assailant who had launched four rocket-propelled grenades and automatic rifle fire at the embassy from a nearby building was later gunned down by security forces who stormed his hideout, police officials said.
Police sources who spoke on condition of anonymity identified the dead assailant as a Palestinian named Ahmed Raja Abou Kharroub.
The sources also confirmed reports that a paper found on the dead attacker claimed the attack was in retaliation for the assault on Chechnya.
State-run television reported the paper said: "In sacrifice for Chechnya." A private radio station, Voice of Free Lebanon, said the paper found on Kharroub was addressed "The Call of Grozny." It was not clear if the reports conflicted or if the paper said both things.
Lebanese army troops and policemen in armored personnel carriers and trucks fanned out in the area shortly after the midday attack at the busy Corniche Mazraa thoroughfare. Troops sealed off neighboring buildings and streets and searched for assailants who fled under heavy rain.
Earlier it appeared the assailants had taken up positions inside the embassy grounds, but it was later found that they had been next door.
After the attack, which lasted only a few minutes, troops carrying assault rifles ordered people indoors as shopkeepers shuttered their stores and evacuated during the search. The cordon was lifted about two hours later.
An official police statement said one policeman and an attacker were killed, and several passers-by were wounded. Police had reportedly earlier that two officers were killed and six others were wounded in the clash.
The Mazraa area is in the Muslim sector of Beirut, where extremists have been sympathetic with fellow Muslims in Chechnya who are fighting an onslaught by Russian forces.
Russian troops launched a military offensive in September to wrest control of the rebel republic after Chechen-based militants invaded a neighboring region and were blamed for ensuing apartment bombings elsewhere in Russia.
It was the most serious attack on a foreign diplomatic mission in Lebanon since the end of the 1975-1990 civil war, during which foreign ationals and embassies as well as ordinary Lebanese were targets of armed factions. During that time, quarrels were frequently settled by gunfire on the streets of the capital.