Republican Gov. Charlie Baker has held his first meeting since taking office with Democratic leaders of the Legislature, with a projected state budget shortfall among the key topics of discussion.

Baker met privately in his office on Monday for more than one hour with House Speaker Robert DeLeo and Senate President Stanley Rosenberg.

The new governor said in his inaugural address last Thursday the shortfall _ which he blamed on excessive spending _ would exceed $500 million. He has ordered a general hiring freeze across state government.

Baker has ruled out cuts in local aid or tax increases to erase the deficit. Rosenberg said after Monday's meeting that while all options are on the table, new taxes would the ``last option.''

Baker said other topics discussed included Boston's Olympic bid.

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