The latest assays are from six holes, and one intersection hit 23.47% copper over 0.4 metres, the company said.
High grade zones were found at both the Mahab 4 and Maqail South areas in Block 5.
Meanwhile, at Block 4, further drilling suggested a larger tonnage, lower grade deposit target.
A broad mineralised zone with 33.4m at 0.69% copper and 0.1g/t gold from 87m, including 4m at 1.56% copper and 5.1m at 1.22% copper, was hit in one hole.
Chief executive David Archer said: "The broad, high grade copper intersections outlined by the drilling underscore the very appealing, early development potential of the Block 4 and 5 licences in Oman.
"The Mahab 4 and Maqail South deposits in Block 5 already have a current indicated and inferred mineral resource of 1.7Mt at 2.2% copper and these recent drill results further underpin our confidence in their potential."
Drilling continues and is expected to be completed before the end of the third quarter, 2016, while a new resource estimate for both Maqail and Mahab 4 will be released in the fourth quarter of 2016.
Savannah has rights to three blocks - four, five and six, covering 1,270 sq km in the copper-rich, Semail Ophiolite Belt in Oman.
Savannah is earning a 65% stake in Al Thuraya LLC, which owns the Block 4 project, and is a 65% shareholder in Al Fairuz Mining, the holder of the Block 5 licence.
Savannah shares added 5.71% in early deals, to stand at 4.625p.