Finance Minister Michael Sarris said he had reached no deal on financing with his Russian counterpart, Anton Siluanov, but talks were continuing.
Cypriot officials disclosed that the country's energy minister was also in Moscow, ostensibly for a tourism exhibition. Cyprus has found big gas reserves in its waters adjoining Israel but has yet to develop them.
"We had a very honest discussion, we've underscored how difficult the situation is," Sarris told reporters after talks with Siluanov. "We'll now continue our discussion to find the solution by which we hope we will be getting some support.
"There were no offers, nothing concrete," he said.
Austria's finance minister made clear the European Central Bank could soon pull the plug on Cypriot banks after the island's parliament rebuffed EU demands for a levy on bank deposits to raise 5.8 billion euros.
Not a single lawmaker voted for a proposed levy that would have taken up to 10 percent from larger accounts, many of which are held by Russians and other foreigners, while sparing small savers with less than 20,000 euros in the bank.
It was the first time a national legislature had rejected the conditions for EU assistance, after three years in which lawmakers in Greece, Ireland, Portugal, Spain and Italy all accepted biting austerity measures to secure aid.
Rejection of the key condition for a 10 billion euro ($12.9 billion) bailout, cast the 17-nation currency bloc into uncharted waters, with a risk of financial contagion to other troubled member states.
However, the EU has a tradition of pressing smaller countries to vote again until they achieve the desired outcome.
President Nicos Anastasiades, barely a month in the job, met party leaders and the governor of the central bank at his office. Government spokesman Christos Stylianides said a "Plan B" was in the works.
"A team of technocrats has gone to the central bank to discuss a plan B related to financing and reducing the 5.8 billion euro amount," he told reporters during a break in the meeting with party leaders. He did not elaborate.
Anastasiades was also due to hold a cabinet meeting and talk with officials from the so-called "troika" of the EU, European Central Bank and International Monetary Fund.
Among the most urgent decisions awaited was whether the government will allow banks to reopen as planned on Thursday and Friday, at the risk of a run of withdrawals, or keep them closed until next week in hopes of a solution. Deputy Central Bank governor Spyros Stavrinakis said no decision had been taken yet.
Cyprus has asked Russia for a five-year extension of an existing loan of 2.5 billion euros that matures in 2016, and a reduction in the 4.5 percent interest rate. Sarris told reporters in Moscow he had also discussed "things beyond that".
Austrian Finance Minister Maria Fekter said the next move was up to Cyprus but the ECB would not keep Cypriot banks afloat indefinitely unless a bailout was agreed.
If Cyprus did not come up with a new plan, Fekter told reporters: "Then the banks won't open on Friday because the ECB will not provide any more liquidity. That is a more horrible scenario than what is on the table now.
"We will certainly help the Cypriots but only under conditions that make sense. Certainly neither the ESM (euro zone bailout fund) nor the ECB can allow a bottomless pit," she said.
Outraged Cypriots had emptied cash machines at the weekend after news broke that they would be taxed on their savings to contribute to the bailout, breaking a taboo in Europe's handling of the stubborn debt saga so far.
The crisis is unprecedented in the history of the divided east Mediterranean island of 1.1 million people, which suffered a war with Turkey and ethnic split in 1974 in which a quarter of its population was internally displaced.
While Brussels has emphasised that the tax measure was a one-off for a country that accounts for just 0.2 percent of Europe's output, fears have grown that savers in other, larger European countries might be spurred to withdraw funds.
Even the Church of Cyprus offered to help.
"The entire wealth of the Church is at the disposal of the country ... so that we can stand on our own two feet and not on those of foreigners," Archbishop Chrysostomos said after meeting Anastasiades early on Wednesday,
The Church of Cyprus is a major shareholder in Cyprus's third-largest domestic lender, Hellenic Bank
Leaders of the currency union said the bailout offer still stood, provided the conditions were met.
The ECB had threatened to end emergency lending assistance for teetering Cypriot banks, crippled by their exposure to the financial crisis in neighbouring Greece.
Euro zone paymaster Germany, facing an election this year and increasingly frustrated with the mounting cost of bailing out its southern partners, said Cyprus had no one to blame but itself.
"For an aid programme we need a calculable way for Cyprus to be able to return to the financial markets. For that, Cyprus's debts are too high," said Germany's finance minister, Wolfgang Schaeuble.
With Sarris and Energy Minister George Lakkotrypis in Moscow, there was mounting speculation that Russian oil and gas giant Gazprom had mooted its own assistance plan in exchange for exploration rights to Cyprus's offshore gas deposits.
Noble Energy reported a natural gas recovery of 5 to 8 trillion cubic feet of gas south of Cyprus in late 2011, in the island's first foray to tap offshore resources.
Russian authorities have denied the Kremlin plans to offer more money.
A senior source in the "troika" said dealing with Cyprus was even more frustrating than protracted wrangling with Greece.
"The Greeks wanted to cheat on you all the time, but they knew what they wanted. The Cypriots are leaving us really confused," the source said.
(Additional reporting by Lionel Laurent, Noah Barkin, Gilbert Kreijger, Adrian Croft, Steven C. Johnson, Robin Emmott, Michael Shields and Lidia Kelly. Writing by Matt Robinson and Paul Taylor, editing by Mike Peacock/Anna Willard)