"We cannot but use this visit to discuss bilateral relations and the most problematic points, by which I mean Ukraine and Syria and maybe some other regions," Putin told Merkel at the start of the meeting in the Black Sea resort city of Sochi.
The Russian and German leaders have scaled back links as Moscow's ties with the EU plunged to a post-Cold War low over the crisis in Ukraine.
Berlin has said Tuesday's meeting would "above all" focus on the upcoming G20 summit in Hamburg in July and no breakthroughs were expected on major disagreements, although Putin earlier called for ties "to fully normalise."
Merkel has strongly backed EU sanctions on Russia for seizing Crimea from Ukraine in 2014 and supporting the pro-Kremlin separatist insurgency in the east of the country.
Moscow has responded with an embargo on agricultural products from the West. A European-brokered peace plan to end the conflict has hit a dead end.
The German leader last visited Russia in May 2015 when she met Putin in Moscow but, like most Western leaders, snubbed a Red Square parade for the 70th anniversary of World War II victory.
Merkel has been the main mediator with Putin over the crisis in Ukraine. She is a key proponent of keeping sanctions on Moscow in place until a stalled peace plan to end the conflict in Europe's backyard is fulfilled.
Merkel and Putin have taken part in a number of four-way meetings, most recently last October, with Ukrainian President Petro Poroshenko and France's Francois Hollande aimed at implementing the plan the four countries hammered out in February 2015.
Last month, Merkel and Putin participated in a four-way phone conversation with Poroshenko and Hollande, agreeing to step up the peace deal's implementation.
"There are two topics that weigh down relations... the annexation of Crimea contrary to international law and then the destabilisation of eastern Ukraine by pro-Russian separatists," Merkel spokesman Steffen Seibert told journalists ahead of the visit.
Both sides have also said the talks will cover the conflict in Syria, where Putin's military backing for leader Bashar al-Assad has set him at odds with the West.
In her first official visit to Russia last week, EU foreign affairs chief Federica Mogherini insisted that cooperation between the two sides was "not frozen" but said progress was hampered by profound disagreements on subjects including Ukraine and Syria.
'Diplomatic ice age thawing'
The G20 is now the only format for Russia to meet the other major international powers after its exclusion from the G8, now the G7.
At the G20 summit, Putin is expected to meet US President Donald Trump. Immediately after meeting Merkel the Kremlin strongman is set to hold his third phone call with Trump.
Merkel visited Saudi Arabia on Sunday for talks focusing on preparations for the G20.
German broadcaster Deutsche Welle suggested ahead of Merkel's visit that "the diplomatic ice age... might be nearing an end" as it sends "a strong diplomatic signal" of both sides' willingness to engage.
The leaders are set to hold a press conference at 1230 GMT between two rounds of talks, Seibert said.
Turkish President Recep Tayyip Erdogan is also due to meet Putin in Sochi on Wednesday. The two leaders have inched closer together on Syria as Erdogan's ties with Europe have plummeted.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
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