Logan's first response upon seeing MJ, in ASM, was something along the lines of, "What's a babe like her doin' with a geek like you?" Kind of the same attitude he has/had toward the Jean/Scott relationship, just replace 'geek' with 'tight@$$'. We all know how that went.
Next encounter was during that terrible arc in MK: Spider-Man. Peter comes home to Stark Tower to find Logan hanging out with his wife, staring at her with a smirk on his face. The conversation goes something like this:
PP: Oh nothing...except I get home from work and find Avengers hanging out in my home like it's a singles' bar!
L: You're out of line there, bub. I don't do that.
PP: Oh, yeah? Can Scott Summers confirm that for me?
That's gotta be one of my most-loved comebacks of all times.
In the next issue, during a training exercise, Wolverine 'accidentally' stabs Peter in the gut. Never mind that Peter is faster, more agile, and has a danger sense, Logan is just that good.
But back on topic, I'm not saying that Logan was necessarily trying to kill Peter, but these are two guys that have fought before and Logan has clearly expressed an interest in MJ at this point. And unlike Scott, Peter refused to sit by and take it, so how did Wolvey react? With violence, the only way I've ever seen him do so.
There were some other incidents, most notably when MJ was caught sneaking into Stark Tower and Wolverine made the mistake of bad-mouthing her to Peter. For that, he was punched through an 'unbreakable' glass window. The most notable one would be during "The Other" storyline, where Logan asks MJ out after Peter dies as a way of giving her a place to channel her anger and grief. Again, you suddenly have this 'honor' that is totally out of place compared to his past actions.
Okay, I'll let you guys (and girls) get back to your Wolverine-centric talk now. I wouldn't want to hijack his thread.