Pakistan were 89-1 when bad light stopped play early and stumps were called on day four in Galle with left-handed opener Imam-ul-Haq on 46 and skipper Babar Azam on 26.
The arrival of rain ended any chances of play, adding to Pakistan's hopes of a draw to clinch the two-match series, which they lead 1-0.
But the tourists will need to make an unprecedented chase -- with another 419 runs needed to win -- if they are to make it 2-0.
The West Indies hold the record for the highest successful Test chase with 418 against Australia in 2003 at Antigua. Sri Lanka, who declared their second innings on 360-8 in the second session after resuming on 176-5, need nine wickets on the final day to end the series level.
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