The 3-0 whitewash in South Africa triggered speculation about Mathews' future as captain but SLC believes the all-rounder can rebuild the team which still remain in the throes of a transition since stalwarts Kumar Sangakkara and Mahela Jayawardene quit international cricket in 2015.
"Angelo has our fullest backing. We are looking at him leading us at the 2019 World Cup," SLC president Thilanga Sumathipala told reporters on Thursday.
"We have some aggressive plans leading up to the T20s and ODIs (in South Africa). Angelo is a kind of guy who takes responsibility and we are confident that he will help the team turn things around," Sumathipala added.
Chief selector Sanath Jayasuriya blamed the loss in South Africa to inexperience and urged patience.
"As the Sri Lanka team is full of young blood, it is not a surprise that they faced a setback in South Africa," the former captain said. "This is not a time to blame and destroy Mathews' captaincy. This is a time when we have to strengthen Mathews.
"As a former captain I know how these allegations can badly affect Mathews' morale, especially during a series.
"We have to support Mathews, correct our faults and face the T20I and ODI series with confidence."
(Reporting by Amlan Chakraborty in New Delhi; editing by Sudipto Ganguly)
