~25% of the murders in the US are already committed without guns, so even if you removed gun crime outright and no one decided to commit the same crime with a different weapon, the US would still have ~2x the murder rate of Europe. Not that this is a case against gun control, as we're still (very theoretically) saving ~15,000 lives a year. But it does suggest that there is a cause for the differing rates that is not related to guns.
Here's the murder weapon statistics for 2019 from the FBI[1]. This only includes homicides for which the weapon is known. We'll assume that the rest match the distribution, though I suspect if you can't identify the weapon, there probably aren't bullet holes.
Summing total homicides gives 13,927. Summing total firearm homicides gives 10,258. 10,258/13,927 = 77.15%. I admit I did not do initially do that work and instead summed percentages from this infographic[2], arriving at 26.3% non-firearm homicide. I can't explain the discrepancy, as they point to the same data. The total homicide count is 5 higher on the FBI site, so possibly the page was updated later on. I point this out to clarify that I rounded the percentage down, which is why I felt comfortable with .25 * 7 ~= 2, though the answer with the new percentage is 1.59. I'd round to 1.5 if I did it again.
If you want a source for Europe's homicide rate being 1/7 that of the US, you'll have to ask the person I was replying to. Wikipedia[3] says Europe's murder rate is 3.0 and the US is 6.5, but I expect the person here was restricting it to the EU or something else along those lines (also various sources differ, and it's something that changes over time). I don't think the restriction changes either of our points, as long as the 7x number does really exist.
I can't recall ever having seen an NRA ad but I don't imagine my comment sounds anything like one. If the NRA really does say in their ads that they're not making a case against gun control and that it could save 15,000 lives a year, I don't have a problem sounding like them.