As a result there have been a number of reports of people in the UK switching their funds from British banks to Irish institutions.
Ms Lagarde said "a measure decided in one [European Union] member state has to be shared in advance with other member states".
"Because when something happens in one member state it affects everybody else around, so there needs to be that level of cross-sharing of information," she added.
European Union Competition Commissioner Neelie Kroes said on Wednesday that she urged national governments "not to act unilaterally".
"It is a must," she said.
While the Republic of Ireland is currently the only European Union nation to guarantee all bank deposits, Brussels requires that all member states offer a minimum protection of 20,000 euros ($28,100; £15,800).
The UK government has indicated that it plans to raise its own deposit guarantees to £50,000 from the current £35,000 limit.
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