I googled a little something - an actual product that exists on Earth. Now, this product uses a halogen lamp to melt ice, and is advertised to be releasing the same kind of light as the sun.
Why did I bring this up? It's because a single wavelength of light won't be enough to melt ice. What you want is a mix of many different wavelengths, as shown by the graphs here. More importantly, consider the fact that this planet has an atmosphere. If it has an atmosphere as thick as Earth, the device you need needs to somehow disable/remove a part of the atmosphere for a direct hit. Otherwise, you need to consider what happens to the released E&M Radiation once it enters the atmosphere, because that's what's going to melt the ice. Problem with your laser idea is that while you could find the right wavelength to melt the ice, the atmosphere could block those wavelengths. South pole ice, for example, has a low absorbity at between 250-450 nm wavelengths of light, but this is useless if the atmosphere blocks it.
But I think this is all way too complicated. The game Spore has a heat-ray kind of like this that heats up planets to a level at which next-tier plants can grow (which will then stabilize the tier) but I've never liked it. I think what you need is to land something on the planet to heat it from the inside - literally pollute it like we're doing to our planet right now. Maybe some sort of robot that will burn hydrocarbons to the point that it causes global warming. It could take some time, but it could work. If you still like lasers, consider landing the robots to specifically laser the ice off directly, or to use the laser to heat up the atmosphere. Unless you make this large-scale, you also get to control how much of the planet melts this way.
Also consider messing with plate tectonics (if you have that ability). Large-scale volcanism can also be triggered given that it doesn't cause a nuclear winter. All options I've mentioned are very expensive, though.
EDIT: From comments we had a clarification that we are looking to melt a single structure that is covered by ice. For that reason, light between 200-500 nm would be good at melting off the ice if lasered in from within the atmosphere (ideally at a similar altitude/area to the ice, so the laser does not lose energy to other particles).