After scoffing at a decision by the United States and its allies to boycott a planned Group of Eight summit in Sochi and hold a G-7 summit instead without Russia, the Kremlin said it was keen to maintain contact with G8 partners.
"The Russian side continues to be ready to have such contacts at all levels, including the top level. We are interested in such contacts," Putin's spokesman, Dmitry Peskov, told Interfax news agency.
British Prime Minister David Cameron made clear that while the West did not accept Putin's annexation of Crimea, it would hold back from more severe measures against the Russian economy unless he went further.
"There's a view that the status quo is unacceptable, but there's then another very, very strong view that any further steps into Eastern Ukraine would be even more serious and would result in much greater sanctions," Cameron told reporters in The Hague when asked whether the West accepted that Crimea was lost.
Moscow made two conciliatory gestures on Monday as its deputy economy minister said up to $70 billion in capital may have fled his country in the first quarter of the year.
Foreign Minister Sergei Lavrov met his Ukrainian counterpart Andriy Deshchytsia for the first time on the sidelines of a nuclear safety summit in The Hague, even though Russia does not recognize the Kiev government.
Moscow also allowed the first monitors from the pan-European security watchdog OSCE to begin work in Ukraine after prolonged wrangling over their mandate, which Russia says excludes Crimea.
The Ukrainian Foreign Ministry said Deshchytsia protested at the annexation of Crimea. Lavrov said Russia did not intend to use force in eastern and southern regions of Ukraine, and "the two sides agreed not to fuel further escalation in the Crimea problem that could cause casualties", it said.
Ukraine ordered its remaining forces in Crimea to withdraw on Monday for their own safety after Russian forces fired warning shots and used stun grenades when they stormed a marine base and a landing ship. There were no casualties.
That order came too late to save the job of interim Defence Minister Ihor Tenyukh, who was sacked by parliament on Tuesday over his handling of the crisis, after it emerged that less than a quarter of soldiers in Crimea plan to stay in the military.
Lawmakers elected Mykhailo Koval, head of the Ukrainian border guard, to replace Tenyukh.
In the Perevalnoye base, 25 km (15 miles) south east of the capital Simferopol, somber-looking Ukrainian troops loaded a freight truck with furniture, clothes and kitchen appliances.
"We are not fleeing, but leaving to the mainland where we will continue to serve," said a soldier who identified himself only as Svyatoslav. "One cannot be a soldier without a country and we have to relocate," he said.
But in the Belbek air base stormed four days ago, officers and soldiers refused to leave until the Russian military releases their commander, Colonel Yuliy Mamchur, who became a symbol of Ukrainian resistance in Crimea.
According to his aides, Mamchur is being held in the Russian Black Sea Fleet's home port of Sevastopol.
Ukrainian Finance Minister Oleksander Shlapak said he was negotiating with the International Monetary Fund for a loan package of $15-20 billion because the economy had been severely weakened by months of political turmoil and mismanagement. He forecast a 3 percent contraction in the economy this year.
Kiev backed away from a threat to cut off water and electricity supplies to the Black Sea peninsula, which Russia annexed last week despite Ukrainian and Western protests.
Putin's spokesman Peskov reiterated that since the Black Sea fleet was no longer based in what Moscow considers to be Ukrainian territory, there were no legal grounds for continuing to give Ukraine a discount in the price it pays for Russian gas, especially since Kiev was not paying its arrears.
(Read more: German businesses unsettled by Crimea tensions)