London - Sri Lanka were set a target of 390 to win the first Test against England at Lord's on Monday's fifth and final day.
Before play resumed, England captain Alastair Cook declared his side's second innings on their overnight score of 267 for eight.
Gary Ballance remained on 104 not out - his maiden Test century.
If Sri Lanka reach their target, it will be the fifth-highest total in the fourth innings to win a Test.
The corresponding Lord's record is the 344 for one, requiring 342, made by the West Indies against England in 1984.
This is the first of a two-match series, with the second Test between England and Sri Lanka starting at Headingley on Friday.