MS incoming student: How to convince my department to give me financial support?
It's almost certainly not possible. The grad school sent you to the department because funding isn't the grad school's job. They don't really know if the department has funds or not. The department's initial response was negative probably because they don't have funds for you. I can only guess at why they've agreed to take a call anyways, but it's probably just because you've been persistent and either a) they are having a hard time saying simply &quot;no&quot;, because it's culturally uncomfortable to say, or b) they think you'll take the &quot;no&quot; answer better over a call or stop bothering them.
There are no secret words; there aren't typically funds for MS students and your rejection for PhD was likely because they've offered the available funding slots to candidates they liked better for the PhD program; you're left as someone they maybe would be okay taking as a PhD student given unlimited funds, but they don't have unlimited funds, so they've offered the MS instead.
A more cynical viewpoint is that they don't really want you at all, but are willing to take any student who is willing to pay the high undiscounted fees that are typically charged to international students.
If you'd like to be a PhD student in the US, you are probably better off applying as a PhD student at other universities.