The proposal was put forward by Communist lawmaker Nikolai Kharitonov.
"I consider it expedient for social unity to hold a minute of silence for all those killed on October 3-4, 1993," he said.
Official figures say that almost 200 people died during clashes in Moscow that broke out as a result of a parliamentary crisis triggered by then-Russian leader, Boris Yeltsin, who on September 21, 1993 dissolved the opposition-led Supreme Soviet and called for new elections.
Unofficial sources say the death toll during the deadliest fighting in Moscow since 1917 may have reached as high as 2,000.
Russian legislators subsequently rejected Yeltsin's decree and voted to impeach him. They also chose and swore in vice-president, Alexander Rutskoi, as acting president.
As anti-Yeltsin protests began on the streets of the capital, rebel ministers and their armed supporters barricaded themselves in the White House, then the seat of the Russian parliament.
On October 2, supporters of the rebel lawmakers built more barricades in the centre of Moscow. The next day, armed anti-Yeltsin groups stormed the police cordon around the White House. Crowds opposed to Yeltsin also took control of the Moscow City Mayor offices as Russia headed toward civil war.
On October 4, Yeltsin ordered the shelling of the White House. There was also heavy fighting, during which 67 people lost their lives, around the Ostankino TV tower in north Moscow as anti-Yeltsin forces attempted to gain control of the airwaves.
State Duma Speaker Boris Gryzlov, a member of the ruling United Russia party, spoke out against the idea of a minute's silence.
"Fifteen years have passed - let's be a little more politically correct with regard to those events," he said, adding that it would be more appropriate to simply listen to what Kharitonov had to say.
The Communist MP noted that among the present lawmakers there were those who had been members of the Supreme Soviet in 1993.
"They may be in different political factions now, but they are perfectly aware of what the events of October 3-4 did," he said.
After the storming of the White House, the seat of the new parliament, known by the tsarist-era name 'Duma,' was moved to another building near Red Square. The White House is now the seat of the Russian government.
