Both batsmen, who had notched up centuries in the first test in Galle, were nearing hundreds again with Dilshan unbeaten on 85 and Sangakkara on 90.
A total of 110 minutes of play was lost due to rain after lunch and four sessions had already been lost in the game in the first three days, making a draw the likeliest outcome.
Sri Lanka is still 373 runs behind Pakistan's first innings score. The home side leads the three match series 1-0 after winning the first test in Galle by 209 runs.