SEOUL (Reuters) - South Korea's economic growth was expected to show little improvement over April-June versus the first quarter in sequential terms, a Reuters poll found on Monday, as weak exports and capital investment continue to undermine growth.

The economy was expected to expand by 0.7 percent in the second quarter from the first on a seasonally adjusted basis, according to the survey, accelerating slightly from 0.5 percent growth in January-March.

Second quarter growth data, if weak, is unlikely to surprise markets as both Bank of Korea Governor Lee Ju-yeol and Finance Minister Yoo Il-ho have expressed concerns of a weakening in private consumption on top of underlying softness in the economy.

"Any growth below 1 percent is troubling. Consumption is weak and the recovery on a whole seems to be slowing," said Chae Hyun-kee, an economist at KTB Securities.

The same poll expected growth in the second quarter of 2.9 percent in annual terms, following a 2.8 percent rise in the first quarter.

A majority of analysts polled said the economy may find some relief in the third quarter as the Bank of Korea cut interest rates in a surprise move in June, and the market consensus is for at least another rate cut by year-end. But any improvement would be slight, analysts say.

"The third quarter is likely to be sluggish as well. If the extra budget is ratified quickly a quick slowdown may be averted but it will be difficult to change the flows of things altogether," said June Park, economist at Daishin Economic Research Institute.

The policy base rate is currently at a record low 1.25 percent after the June rate cut. Earlier this month, the Bank of Korea trimmed its growth forecast for this year to 2.7 percent from 2.8 percent.

The finance ministry will submit a supplementary budget draft of 11 trillion won ($9.69 billion) this week to parliament. The faster lawmakers ratify the budget, the sooner the boost to the economy will be felt.

South Korea's extra budget will focus on creating 68,000 new jobs to make up for severe job cuts as the struggling shipping and building industries are overhauled.

The government has revved up restructuring this year as the trade-reliant economy has seen shipments fall continuously since January 2015.

(Reporting by Yun Hwan Chae, Nataly Pak, Dahee Kim and Jeongeun Lee; Writing by Christine Kim; Editing by Eric Meijer)