* Sales to Russia dry up as rouble down, Sochi spree over
* Steelmakers sell cheap rebar to Algeria
* Stressed mills in southern Europe struggle to compete
* Competition from Turkey heats up as lira down
LONDON, March 5 (Reuters) - Ukraine's steel exporters are trying to push into new markets such as in North Africa as a weak currency, battered by political upheaval and tensions with Russia, has pushed rebar prices to 3 1/2-year lows.
The hryvnia has fallen 11 percent versus the dollar this year as the overthrow of its president and the entry of Russian troops into Crimea have added to Ukraine's long-running financial problems.
Ukraine, the world's second-largest exporter of steel rebar, recently sold the alloy to Algeria, while its prices have fallen some $50 a tonne since the start of the year to $510-$515, industry sources said.
"There's more competition from CIS markets in Ukraine and Belarus, while demand has remained sluggish. That's why Ukraine was selling to Algeria at low prices, just to find a new market," CRU analyst Dmitry Popov said.
By contrast, southern Europe's rebar exports fetch around 440 euros ($610 a tonne), according to CRU, making it tough for European steelmakers to compete even in markets such as Algeria, where a free trade agreement means they do not have to pay a 15 percent export duty.
While Ukraine's rebar prices are often cheaper than Europe's, the current spread of around $100 a tonne is particularly wide.
In 2013, most of Ukraine's rebar went to Russia, but that demand has slumped after the end of the Sochi Olympics building spree and due to a weak rouble, down 10 percent versus the dollar this year.
Meanwhile, competition has been heating up with Turkey, the world's top rebar exporter, where export prices have also fallen sharply thanks to weak domestic demand and strong declines in the Turkish lira.
The flow of commodity shipments out of Ukraine has not yet been disrupted by the tense politics, with its ports handling a total of some 22.7 million tonnes so far this year, roughly equal to the same period last year.
"For the moment there isn't any risk to buy from Ukraine. People are afraid because the situation is complicated, but for the moment everything is running, the ports, everything," a steel trader in Ukraine said.
The move by Ukraine into markets in North Africa is unwelcome news for beleaguered European steelmakers struggling with weak demand, down some 27 percent since 2008, and structural overcapacity of 30-40 million tonnes. ($1 = 0.7225 euros)
(Additional reporting by Alexander Winning in London; editing by Susan Thomas and Jane Baird)