Russia announced it was halting a visa-free regime for Turkish visitors, after threatening a raft of retaliatory economic measures to punish the NATO member state.
Tuesday's incident has sent recriminations flying between two rival players in the Syrian war just as countries such as France are pushing for a broader coalition to try to defeat the Islamic State group.
"We advise Russia not to play with fire," Erdogan said in a speech in Ankara, lashing out at Russia's response to the downing as well as its support of the regime of Syrian President Bashar al-Assad.
But Moscow responded coolly, saying Turkey has yet to apologise for shooting down the jet on the Syrian border.
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Turkey says the Su-24 warplane strayed into its airspace and ignored repeated warnings but Russia insisted it did not cross from Syria.
It is thought to be the first downing of a Russian plane by a NATO member in more than half a century.
One of the pilots was shot dead in Syria after parachuting out of the burning plane while the second was found safe and sound, but one Russian soldier was killed in a rescue operation.
Moscow has ruled out any military response, but has pledged broad measures targeting entire sectors of the Turkish economy including tourism, agriculture and possibly key energy projects.
Lavrov said Turkish nationals would require visas from January 1, after Putin this week warned citizens not to travel to Turkey -- a hugely popular destination for Russians.
"Russia is quite concerned with increasing terrorist threats in the Republic of Turkey," Lavrov added, after a spate of bloody attacks blamed on Islamic State extremists there.
Moscow has also hinted the reprisals could hit two major projects with Turkey -- a planned gas pipeline and a nuclear power plant.