* Finance minister shuts door on supplementary budget plans
* No mention of rates, although market sees possible cut soon (Adds analyst comment, background)
By Christine Kim
SEOUL, July 16 (Reuters) - South Korea's new finance minister and its central bank governor both highlighted weakness in Asia's fourth-largest economy on Wednesday, adding to market expectations that an interest rate cut could be in the offing.
While Finance Minister Choi Kyung-hwan did not mention interest rates in his inauguration speech and shut the door on the prospect for a supplementary budget, he promised a bigger budget next year, citing weakened demand and sluggish output.
Also on Wednesday morning, Bank of Korea Governor Lee Ju-yeol said his assessment of the economy in April, when he said interest rates should rise if the economy kept to its projected growth path, had been too optimistic.
"You can signal a move 23 months prior, but if something unexpected happens in even a month's time that could change policy," Lee told reporters on the sidelines of an event.
The South Korean won was down 0.6 percent as of 0105 GMT following Choi's remarks, after they reinforced views that the government would keep a lid on further gains in the won to support local exporters' price competitiveness.
September futures on three-year treasury bonds rose 0.05 points to trade at 106.81.
"Right now the market sees a rate cut happening no matter what even if the current growth rate doesn't warrant a cut, and if the central bank doesn't lower interest rates that could hurt markets and sentiment," said Park Sang-hyun, chief economist at HI Investment & Securities in Seoul.
"Choi has been around for a long time and judging by his experience he will have more propelling power in terms of policy," Park said of the veteran lawmaker.
However, all but two economists in a Reuters poll last week predicted that the Bank of Korea's next move would be a rate increase.
The central bank has left rates unchanged for 14 months. The last time it moved rates was when it cut them in May 2013, under apparent government pressure.
South Korea's economy has slowed in recent months, as a ferry sinking in April that left more than 300 people dead or missing acted as a drag on already-anaemic domestic spending while exports have been bogged down by weakening demand from China, its biggest market.
The Bank of Korea earlier this month said the economy would expand by 3.8 percent this year, down from its earlier forecast of 4.0 percent.
Ronald Man, an economist at HSBC Hong Kong, told Reuters on Wednesday that the government may run a larger-than-projected budget deficit in 2015, pushing back its target to achieve a balanced budget.
The finance ministry, under Choi, is also expected to speed reform measures, including those aimed at raising the female participation rate in the workforce.
"The importance of domestic consumption is being stressed, but at this point I doubt the government will be able to let their focus on exports weaken," said a foreign exchange dealer at a bank in Seoul.
The dealer said dollar demand from market participants increased on comments from both the central bank governor and finance minister, as expectations for a rate cut grew. (Additional reporting by Yena Park and Taemin Chang; Editing by Tony Munroe and Jacqueline Wong)