* Martinez's Fintech Advisory to retain stake in Tuscan bank
* Monte Paschi aims to choose successor on March 4 (Racasts, adds detail)
ROME/SIENA, Feb 27 (Reuters) - Mexican billionaire David Manuel Martinez has resigned from the board of Banca Monte dei Paschi di Siena after four months in the post but will not sell his 4.5 percent stake in the troubled Italian lender.
Monte Paschi, which is due to launch a 3 billion euro ($3.4 billion) capital increase by June, said Martinez stepped down because he could no longer take part in the board's activities "in a constructive way" because of his executive role at his investment firm Fintech Advisory.
A spokesman for Fintech said the United States-based investment company would not sell its stake in the bank, which was bought in 2014 from the Monte Paschi foundation, the lender's former controlling investor.
A source close to the matter said that Fintech would continue to support Monte Paschi's Chairman Alessandro Profumo and CEO Fabrizio Viola.
Italy's third-largest lender added in a statement that it had already started looking for a successor to Martinez and will take a decision at a board meeting on March 4.
Monte Paschi foundation Chairman Marcello Clarich said the new board member would be a representative of Fintech.
Shares in Monte Paschi rose 1.6 percent on Friday. The stock has gained 27 percent in the past month, underpinned by speculation over potential tie-ups with cooperative banks and investor confidence in the forthcoming cash call.
The bank, which made a fourth consecutive annual loss in is past financial year, had increased the size of the rights issue from 2.5 billion euros to meet tough capital targets set by the European Central Bank. ($1 = 0.8927 euros) (Reporting by Stefano Bernabei, Silvia Ognibene and Danilo Masoni; Editing by Giselda Vagnoni and David Goodman)