* Highest jobless rate in data going back to 1999
* Austerity steps hurting private-sector employers
* Number of Saudi job seekers drops
* Hundreds of thousands of foreigners continue leaving
* Private sector expected to grow only modestly this year (Adds details of Saudi and foreign employment, analysis)
DUBAI, July 5 (Reuters) - Unemployment among Saudi citizens edged up to a record 12.9 percent in the first quarter of this year as private employers struggled under the weight of a new tax and a domestic fuel price hike, official data showed on Thursday.
The figures underlined the difficulties which the government faces as it pushes through reforms to reduce the economy's reliance on oil exports.
The reforms aim to develop non-oil industries and create jobs, but they also involve austerity steps to close a big state budget deficit; a 5 percent value-added tax was imposed at the start of 2018. The austerity is hurting many private companies.
The first-quarter unemployment rate was the highest recorded by the official statistics agency in data going back to 1999. It exceeded the 12.8 percent level which had prevailed for the previous three quarters.
Authorities are keen to lure more Saudis, especially Saudi women, into the labour force to make the economy more efficient and reduce the government's financial burden.
The latest data showed little progress in that area, however, with the number of Saudi job seekers falling to 1.07 million in the first quarter from 1.09 million in the previous quarter, even as the number of employed Saudis also declined.
The figures revealed a continued exodus of hundreds of thousands of foreign workers from Saudi Arabia because of the weak economy and hikes in fees which companies must pay the government to hire expatriates.
The number of foreigners employed in the kingdom shrank to 10.18 million from 10.42 million in the previous quarter and 10.85 million in the first quarter of 2017 - a drop which is slowing the economy by hurting consumer demand.
Saudi gross domestic product, adjusted for inflation, grew 1.2 percent from a year earlier in the first quarter of 2018, beginning to recover after shrinking in 2017, figures released earlier this week showed.
But the rebound was largely due to stabilising oil output, and economists expect the oil sector to lead growth later this year with non-oil businesses expanding only modestly - a trend that may keep unemployment high. (Reporting by Andrew Torchia Editing by Alison Williams)