"We want to improve our performance in the Tests after our recent good showing in the one-day matches," 22-year-old middle-order batsman told reporters here at the official launch of the series.
The right hander, who hit a debut century against Sri Lanka in 2001 to become the youngest batsman to ever achieve the feat in Test cricket, said he was looking forward to the challenge of leading Bangladesh in the Test series.
"Results do not matter to us, we need improvement in Test cricket," he said.
Ashraful, who was named captain earlier this month, was the highest scorer for Bangladesh in the World Cup, hitting 83 balls for 87 runs to help lead his team to a stunning victory over South Africa.
Bangladesh have just a solitary win in 46 Tests since becoming a Test-playing nation in 2000.
Sri Lanka captain Mahela Jayawardene paid tribute to the improved standing of the Bangladeshis in world cricket.
"We all know how good they can be and how dangerous they can be especially after the World Cup. Our guys are keen to do well because Test cricket is the ultimate challenge," Jayawardene said.
Sri Lanka plan to use the series to test a few younger players now that several seniors such as Sanath Jayasuriya and Marvan Atapattu are not available.
"It will be a great challenge to maintain our recent high standards. We need to groom a few younger players," the Sri Lanka captain said.
Jayasuriya is considered only for the one dayers and Marvan Atapattu who was picked for the Tests has made himself unavailable.
This should pave the way for Malinda Warnapura to open the batting with Upul Tharanga.
The three-match Test series begins on June 25, while the three-match one day international series starts on July 20.