(Adds response from Puerto Rico government)

By Nick Brown

NEW YORK, May 10 (Reuters) - Puerto Rico's federally appointed oversight board on Thursday rejected the U.S. territory's budget proposal for next fiscal year, saying it did not comply with a financial turnaround plan for the island approved by the board last month.

In a letter to Governor Ricardo Rossello, the board said the budget's expense projections were inconsistent with the turnaround plan, which is designed to be a blueprint for how Puerto Rico will recover from the twin challenges of bankruptcy and September's Hurricane Maria.

The board directed Rossello to submit a compliant budget by May 15.

Puerto Rico has $120 billion in combined bond and pension debt it cannot pay, the biggest insolvency in U.S. government history. The board on April 19 approved a fiscal turnaround plan that included pension cuts and labor reforms, which Rossello has said he will refuse to implement.

The plan forecasts $6.7 billion in debt payment ability for Puerto Rico through fiscal year 2023. But Rossello's proposed budget does not allocate for debt service, while including other expenses that are not in the plan, like $100 million in municipal spending.

The budget also did not eliminate Christmas bonuses for public servants or include labor reforms demanded by the board.

If Rossello refuses to implement parts of the plan, the board could sue for enforcement, putting yet another piece of the embattled island's financial future in the hands of a judge.

Thursday's letter escalated a war of words between the board and Rossello's administration.

The board criticized Puerto Rican officials who had earlier accused it of failing to consult with the government on a timeline for budget development, saying it had "shared more than seven letters on the topic with various government officials."

Puerto Rico Public Affairs Secretary Ramon Rosario Cortes said in a statement on Thursday night that the board dislikes the plan because it does not include an increased budget for the board's own expenses.

"An increase in the $60 million that they already have is not justified," Rosario Cortes said.

He added, "We reject any attempt by the to acquire powers it does not possess through joint budget resolutions," invoking a longstanding position in the Rossello administration that the board is attempting to encroach on the island's right to make its own laws.

(Reporting by Nick Brown; Editing by Cynthia Osterman)