The Emir, Sheikh Tamim bin Hamad al-Thani, met with Woods and ExxonMobil Qatar General Manager Alistair Routledge at the Al-Bahar Palace.
Qatar and Exxon have had development agreements for more than a decade, with Exxon helping Qatar to become the world's largest LNG exporter. Exxon, working with government-controlled energy company Qatar Petroleum, has invested in LNG-processing plants, transport ships and related infrastructure.
Exxon announced earlier this month that production and exports of LNG from Qatar have not been affected by the row.
The growing diplomatic dispute has raised concerns about global access to Qatar's LNG.
