Prime minister David Cameron discussed the financial crisis in Cyprus with Russian President Vladimir Putin in a phone call on Friday morning.
The call came as authorities on the Mediterranean island sought to convince international lenders to provide the money Cyprus needs to avoid bankruptcy within days.
Cypriot efforts to clinch a contribution from Moscow appear to have failed after Russia's finance minister was quoted as saying talks had broken down. The Kremlin has a significant interest in the situation, because Russian depositors are believed to have around £17 billion in Cypriot banks.
Downing Street said that Cameron and Putin "agreed that they hoped a solution could be found to the crisis", but added that Cyprus took up only a small part of the 30-minute call, which also touched on Syria, the upcoming G8 and G20 summits in Northern Ireland and St Petersburg and BP's Arctic oil deal with Russian company Rosneft.
Cypriot MPs are discussing plans to restructure the country's second largest lender, Laiki bank, as part of a plan to raise up to €5.8b (£4.9bn) to secure a larger rescue package of another €10bn (£8.5bn) from the other 16 eurozone nations and the International Monetary Fund.
A new package is necessary after the parliament in Nicosia rejected a plan this week to grab up to 10% of bank deposits. Banks have remained closed for fear of queues of depositors withdrawing their savings.
The UK government has said it will guarantee the savings of British Armed Forces personnel and civil servants posted to the island, and on Tuesday an RAF plane carried one million euros (£850,000) to Cyprus as a "contingency measure" for troops and their families in case cash machines stop working.
Asked on Friday whether any help was being considered for other British nationals, a Downing Street spokesman said: "Obviously we understand that developments in Cyprus will be worrying for British nationals with savings in Cyprus. We would encourage British nationals who are experiencing difficulties to contact their bank."
Anyone planning a holiday in Cyprus over Easter should keep in touch with Foreign Office advice, which is being kept under review, said the spokesman.
After updated advice yesterday, the Foreign Office website does not caution against travel to Cyprus, but warns: "Cyprus is implementing measures to protect its banking sector. Check with your bank for further information.
"The government of Cyprus has announced an extended bank closure. ATMs, debit and credit cards can be used as normal; however, while banks are closed, we advise taking sufficient euros to cover the duration of your stay, alongside appropriate security precautions against theft."
The Downing Street spokesman said the UK regards the situation in Cyprus as "essentially a matter for the eurozone".
He added: "The situation in Cyprus remains fluid, but it is in all of our interests that Cyprus tackles its difficulties and its banks are stable.
"We will keep the situation under review."