By Emma Simpson
BBC News, Moscow
Last week the White House, this week the Kremlin.
Mrs Merkel spoke of a business-like partnership with Moscow
German Chancellor Angela Merkel's meeting with President Vladmir Putin though went on much longer than planned, an indication perhaps that the two leaders are off to a good start in this new chapter of German/Russian relations.
The signs are that this relationship is going to be a much cooler, more business-like partnership compared with Mrs Merkel's predecessor, Gerhard Schroeder, who developed a close relationship with Mr Putin.
Mrs Merkel is fluent in Russian, having grown up behind the Iron Curtain in communist East Germany, an upbringing that may lead her to take a more sober approach to Mr Putin, who himself is a former KGB officer who served in East Germany.
Just before she left, Mrs Merkel told a German newspaper that a strategic partnership, not friendship, would be the best way to describe Germany's relations with Russia.
And unlike Mr Schroeder, she didn't shy away from tackling sensitive areas like Chechnya and democracy in Mr Putin's Russia.
On the Chechen conflict, she said they discussed the matter in "great detail", adding that it "took us time to find common ground".
As for Mr Putin, he said that he was interested in a constructive, open and friendly discussion of these issues.
That's diplo-speak for quite a heated discussion.
Mrs Merkel arrived here in Moscow just weeks after Russia's nasty gas dispute with Ukraine, which sent a shiver across Europe as supplies were abruptly turned off to its neighbour.
Energy security has quickly moved up the agenda in Western capitals. And Germany is more dependent than most on Russian gas - it gets a third of its gas supplies from Russia.
Whilst Mr Schroeder cultivated a strong energy alliance with Russia, Mrs Merkel has been talking about the need to diversify energy sources.
But Mrs Merkel knows she needs to keep relations on an even keel. The two countries' economies are increasingly entwined.
Russia needs to sell its gas and Germany is one of its biggest customers. And there's about $32bn (£20bn) worth of trade at stake, too.
Both leaders spoke glowingly about their close economic ties and how they could be strengthened. One of the biggest joint projects under way is the North European Gas Pipeline, a route that will bypass Ukraine and the Baltic states, transporting Russian gas direct to Germany.
Mr Schroeder recently accepted the chairmanship of this project, a move that caused considerable controversy since it was a project that he approved whilst in office.
Mrs Merkel spent a fair amount of time discussing the project during the meeting, saying later that it was "an investment in the energy security of Europe".
With tensions escalating over Iran, the focus of these talks inevitably was on what should be done about its controversial nuclear programme.
Analysts had expected Mrs Merkel, fresh from her talks with US President George W Bush, to urge Mr Putin to stand with the West in supporting Iran's referral to the UN Security Council.
The Russian president didn't rule this out, but he also urged caution.
"We need to move very carefully in this area," he said. "I personally do not allow myself a single careless announcement, and do not allow the foreign ministry to make a single uncertain step."
Russia has strong business ties with Iran and is helping to build a $1bn nuclear power plant there. President Putin said that Iran hadn't excluded the possibility of Russia enriching uranium on its behalf.
This was a Russian proposal put forward last year, and was welcomed by the West as a possible way out of the crisis.
If it were to succeed, it would bring considerable diplomatic kudos to Russia and allow it continue its trade with Iran.
Perhaps it's wishful thinking, but Russia still believes its enrichment proposal has some mileage.
Either way, Russia's position, with its UN right of veto, is going to be crucial in the coming weeks.