* Govt FY2019 estimates for CPI, GDP growth both +1.5 pct
* CPI projections suggest gradual progress on ending deflation
* Analyst suspects govt may underestimate uncertain outlook
* BOJ seen cutting inflation projections at July rate review (Adds analyst's quote, detail on projections)
TOKYO, July 6 (Reuters) - Japan's government is set to forecast overall consumer price growth of 1.5 percent in the fiscal year that starts in April 2019, a draft document obtained by Reuters showed on Friday, indicating some progress towards an end to deflation.
The Cabinet Office's projections, due to be submitted to the Council on Economic and Fiscal Policy - government's top economic panel - on Friday, showed the economy likely to grow 1.5 percent in price-adjusted real terms in fiscal 2019. It is expected to expand 2.8 percent in nominal terms.
The government's growth and inflation projections were more bullish than private-sector estimates.
Market economists expect the economy to grow just 0.8 percent in the fiscal 2019, due in part to the impacts from a planned sales tax hike, and they see core consumer prices rising 1.0 percent.
"The government's projections seem to underestimate uncertainty over global economy and domestic labour shortages," said Yoshimasa Maruyama, chief market economist at SMBC Nikko Securities.
"A trade war between the United States and its trade partners could weigh on global growth, which would in turn exert downward pressure on Japan's export-led economy."
The government's inflation projections compare with the central bank's forecast for core consumer price growth of 1.8 percent in fiscal 2019.
The Bank of Japan is likely to cut its price growth forecasts at a policy meeting later this month as long-term inflation expectations stall, sources said, highlighting the bank's difficulty in hitting its elusive 2 percent price target.
For the current fiscal year that started in April, the Cabinet Office is set to keep its overall consumer price growth forecast at 1.1 percent, unchanged from its estimate at the start of this year, the draft document showed.
The jobless rate is expected to fall to a 26-year low of 2.4 percent in the fiscal 2019, reflecting the tight labour market.
The Cabinet Office is set to cut growth projections for fiscal 2018 to 1.5 percent in real terms from 1.8 percent seen earlier, and to 1.7 percent in nominal terms from an earlier forecast of 2.5 percent, due partly to a slowdown in housing investment.
The Cabinet Office issues twice-yearly growth and price projections to provide a basis for guiding economic policy and compiling the annual state budget. (Reporting by Takaya Yamaguchi and Tetsushi Kajimoto Editing by Chris Gallagher)