The meeting, at Mr Putin's summer residence in Sochi, comes with bilateral relations in a trough over the war in Syria and Russia's annexation of Crimea.

They are to discuss both issues but no breakthroughs are expected.

Mr Putin will then meet Turkish leader Recep Tayyip Erdogan on Wednesday.

"Of course, we cannot but take advantage of this visit and discuss bilateral relations and the most problematic points, by which I mean Ukraine, Syria and possibly some other regions," Mr Putin said at the start of the talks with Mrs Merkel, quoted by Russia's Interfax news agency.

Ties between Russia and Germany have worsened since Russia's 2014 annexation of Crimea in Ukraine, with Germany being a driving force behind the EU sanctions imposed in response.

The pair, who are among the most powerful world leaders, have met a number of times outside Russia over the past two years - most recently in October to discuss Ukraine along with Ukrainian President Petro Poroshenko and French President François Hollande.

What will they talk about?

The official purpose is to discuss the G20 summit of world leaders to be held in Hamburg in July. This is now the only forum for Russia to meet other powers, after its exclusion from the G8 (now the G7) over Crimea.

Mrs Merkel wants Russia to seek an end to the conflict in Ukraine by using its influence on pro-Russian separatists, and also needs Moscow's co-operation to reach a peace deal in Syria, says the BBC correspondent in Berlin, Damien McGuinness.

Berlin has been the driving force behind keeping Europe united on sanctions so Russia's only hope of sanctions being lifted, is with German support., our correspondent adds.

Mr Putin is also keen to hear her opinion of US President Donald Trump, whom she recently met.

The situation in Libya, beset by chaos since Muammar Gaddafi was overthrown in 2011, is also on their agenda, Russian media report.

What are bilateral relations like?

As two of the world's most powerful long-serving leaders, the pair have long experience in dealing with each other.

They spoke frequently before the breakdown in communications since 2014, and were said to have a grudging respect for one another.

She speaks Russian, having grown up in communist East Germany, and he speaks German, from his years working for the KGB in Dresden, in the same country, in the 1980s.

But both sides have downplayed the prospect of breakthroughs during their meeting in Sochi.

As well as their opposition over Crimea and Syria, the German domestic intelligence agency has also accused Russia of being behind a series of cyber attacks on state computer systems.

Russian-linked hackers are also suspected to have been behind a direct attack on Mrs Merkel's own Christian Democratic Union party.

Mrs Merkel will also be keenly aware of the growing evidence of intervention from Russian-backed groups trying to spread influence in the domestic sphere, for instance, as she seeks a fourth term in federal elections on 24 September.

What about Mr Putin's other encounters this week?

In contrast, Mr Putin's scheduled meeting with the Turkish president the following day comes at a time of increased co-operation between the two nations.

While they back opposing sides in Syria's civil war - with Moscow supporting Syrian President Bashar al-Assad, and Ankara his opponents - the two countries began carrying out joint air strikes against the so-called Islamic State in January.

The joint operation came a little over a year after Turkey shot down a Russian military jet, resulting in a crisis in bilateral relations.

US President Donald Trump is also scheduled to speak to President Putin by phone on Tuesday, the White House announced on Monday night. They are expected to discuss the war in Syria.

US ties with Russia had been expected to improve with the election of Mr Trump but were hit by Moscow's use of a veto to protect Syria at the UN Security Council following a suspected chemical attack on a rebel-held Syrian town.