Gerrard reached the milestone in Liverpool's 1-1 draw with Newcastle United this afternoon, a game in which Suarez scored an equaliser for his side.
"Such a pity we didn't get the 3 points! Congratulations to Steven Gerrard for his 600 official matches!!" Suarez wrote on his Twitter page.
Stoke City midfielder Charlie Adam, a former teammate of Gerrard, also congratulated the England skipper on his achievement, tweeting: "Congrats to Steven Gerrard 600 games. One of the best players to have played in premier league."
Gerrard's tally puts him 10th in the list of highest appearance makers in Liverpool history, 20 behind Alan Hansen.