The Russian and German leaders have scaled back links as Moscow's ties with the EU have plunged to a post-Cold War low.
Merkel has strongly backed EU sanctions on Moscow for seizing Crimea from Ukraine in 2014 and backing the pro- Russian separatist insurgency in the east of the country.
Moscow has responded with an embargo on agricultural products from 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 that progress was hampered by profound disagreements on subjects including Ukraine and Syria.
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Merkel 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.
Berlin and Moscow said Tuesday's talks agenda includes preparations for July's G20 summit in Germany as well as Ukraine and Syria.
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.
Last month, Merkel and Putin took part in a four-way phone conversation with Poroshenko and Hollande, agreeing to step up implementation of the peace deal.
"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.
Kiev and the West accuse Moscow of giving military support to the rebels in eastern Ukraine, a charge it denies.
He said the leaders would also prepare for the upcoming G20 meeting in Hamburg in July, while a German government source told AFP the visit would be "above all about the G20.