FRANKFURT (Reuters) - European Central Bank policymakers on Friday lined up in support of an interest rate cut in the coming months as inflation in the euro zone falls faster than they had anticipated.

Central bank governors from Germany, France, Finland and Lithuania all talked up the chances of the ECB lowering borrowing costs from record highs, firming up a hint dropped by ECB President Christine Lagarde on Thursday.

They only slightly differed about the timing of a first move.

"The probability is increasing that we could possibly see a rate cut before the summer break," Bundesbank President Joachim Nagel told German podcast Table Today.

His words carry particular weight because Nagel - as is historically the case for a Bundesbank president - has been among policy hawks urging against a hasty rate reduction.

The ECB has three meetings before its summer recess, on April 11, June 6 and July 18.

Banque de France head Francois Villeroy de Galhau, a centrist, said a rate cut should happen in the spring, which he added was "from April until June 21".

Finland's Olli Rehn also said the discussion about lowering rates would resume "in the upcoming April and June meetings".

Their Lithuanian colleague was more explicit, saying that a rate reduction in June was "very likely" and could be the first of a series of cuts worth 25 basis points each.

"In my evaluation, June is the month when really a rate decrease is very likely," Gediminas Simkus told reporters in Vilnius.

The probability of a move in April was "low", he added.

After this raft of comments, euro zone financial markets fully priced in a rate cut in June, followed by three more by December, which would take the 4% rate that the ECB pays on bank deposits to 3.0%.

The ECB cut its projections for growth and inflation on Thursday and Lagarde said the central bank would have "a lot" of the information it needs to decide on a rate cut in June.

Investors have been doubtful that the ECB would move before the U.S. Federal Reserve, citing historical precedents. The Fed is expected to cut its own key rate on June 12.

But Finnish governor Olli Rehn dismissed any such consideration.

"The ECB is not the Fed's '13th Federal District', i.e., one regional central bank," he said in a blog post.

(Reporting By Francesco Canepa; Editing by Emelia Sithole-Matarise)