31 words
This question is somewhat complicated by textual variants & minor changes in inflection, but a pretty safe answer would be the agreement found discussing the fates of the disciples in Matthew 10:21-22 & Mark 13:12-13. The first two words are different, after that the two texts are identical for 31 words:
Matthew 10:
21 παραδωσει δε αδελφος αδελφον εις θανατον και πατηρ τεκνον και επαναστησονται τεκνα επι γονεις και θανατωσουσιν αυτους
22 και εσεσθε μισουμενοι υπο παντων δια το ονομα μου ο δε υπομεινας εις τελος ουτος σωθησεται
Mark 13:
12 και παραδωσει αδελφος αδελφον εις θανατον και πατηρ τεκνον και επαναστησονται τεκνα επι γονεις και θανατωσουσιν αυτους
13 και εσεσθε μισουμενοι υπο παντων δια το ονομα μου ο δε υπομεινας εις τελος ουτος σωθησεται
A table of agreements for 16 or more sequential words is found on p. 320 here
Almost uninterrupted sequences becomes a bit more subjective -- the way this is generally analyzed is by comparing the % of agreement in wording across a long string of text. See an example of this on pp. 21-22 here.