Sri Lanka, replying to Pakistan's 551-6 declared, were 70-1 at lunch with Tillakaratne Dilshan on 46 and Kumar Sangakkara on 22.
Wet weather allowed just 44 overs to be bowled on Sunday and more rain has been forecast for the next two days.
Sri Lanka lead the three-match series 1-0, having won the first Test in Galle by 209 runs.
The third Test will be played in Pallekele from July 8.