Were the direct references to Die Hard and Under Siege made on purpose?

Antoine Fuqua and Gerard Butler both discussed this in a video interview, showing they were definitely aware of the Die Hard connection and they both loved Bruce Willis' works. In fact, they viewed it as the daddy of all action films.

Paraphrasing from the interview, they both drew distinct differences between Die Hard and Olympus Has Fallen, discussing how their film takes place in the White House, with terrorists attacking the White House, on a much bigger scale than Die Hard presented. They also commented on how the undertone of the film was far more serious. It included "without a doubt ... those Die Hard quips", but ultimately takes place in a post 9/11 world and thus simply had to be more mature.

Dylan McDermott, an actor in the film, also said this in an interview:

Interviewer: I'm sure by now you've heard Olympus Has Fallen described as “Die Hard in the White House,” was that a reference that was talked about on set?

McDermott: I had heard that before. That was kind of like the selling point. I'm trying to make different movies so obviously The Campaign, which was a comedy, and Olympus is action movie, and even my work on American Horror Story. So you know, I’m just trying to mix it up as much as possible, create new characters and just keep showing up in the right movies with the right actors, and great directors.

Neither interview mentioned references to Under Siege, but as it was one of the many films that came in the aftermath of Die Hard and was largely a clone of it, all roads effectively lead back to Die Hard.

Therefore, ultimately, they were unquestionably aware of Die Hard and the relationship between their movie and it and so it's certainly plausible that they included direct references (described in the video interview as Die Hard quips). They don't mention any of these quips explicitly, but given their desire to have Die Hard-esque moments, it's definitely possible and arguably likely they paid tribute to it.