Her letter comes after Wikileaks published a transcript of IMF officials discussing bailout negotiations.
One says a "crisis" could force a deal.
Greece publicly demanded an explanation after the leak, suggesting the comments meant the IMF could be planning to deliberately prolong debt negotiations until the country was close to running out of money.
Ms Lagarde said the "incident" had made her "concerned as to whether we can indeed achieve progress", but said she had decided to allow the IMF team to return to Athens to continue debt discussions.
`Robust growth`
However, she also warned that the latest bailout deal was "still a good distance away".
She said that the IMF could only support a deal that would enable "robust growth" for Greece, while also allowing it to tackle its debt repayments.
Last year, Greece agreed a multi-billion dollar bailout with the EU and IMF that was needed for the country to avoid bankruptcy and stay in the eurozone.
Talks between Greece, the EU and the IMF on a bailout review, assessing Greece`s progress at implementing money-saving reforms and aimed at unlocking further loans, are due to resume this week.
The review has been suspended twice since January due to disagreement among the lenders over the estimated size of Greece`s fiscal gap by 2018, as well as different opinions on pension reforms and how bad loans are being managed.
"In the interest of the Greek people, we need to bring these negotiations to a speedy conclusion," wrote Ms Lagarde.
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