It depends on how exactly you mean, but in general, sure. Why not? If genetic tinkering can make the lives of humans or animals better then I see no reason not to.

No one is interested in saving endangered species unless it is in some way lucrative. Very few GMO's belong to the public domain. Even if there are public domain GMOs, a lot of folks are scared of them.

Banana plants are a case where genetic modification is most important. Cavendish is the banana you know, is basically one genetically-locked cultivar (apart from ongoing mutation between populations). 99% of banana exports to wealthier nations are Cavendish. The Cavendish replaced the Gro Michel (supposedly better tasting) when a fungus knocked them out. The only way to save the Cavendish is probably through GMO. Fortunately there is no way a company can really patent it without enforcing patent rights, by engineering some kind of auto-destruct sequence into the plants (if this is possible). These bananas are grown through vegetative propagation only, like the scions of a graft (ex. Orange or Apple varieties), so it makes it easy to steal if such organisms become proprietary.

In Hawaii the papaya industry was saved by our State University by genetic modification. It was a gift to farmers. I'm not sure what the trick is to getting a truly organic papaya, that is how widespread the introduced gene is in populations. No one is going through the expense of testing to see which papayas carry the gene (though I could be totally wrong). The expense to farmers would be absurd since the industry is so small.

What endangered species needs to be saved? Biodiversity is like tool diversity, the more tools you have in your tool shed, the more stuff you can do.

I believe public GMOs (given to all peoples) are possibly a useful tool for retaining the planets biodiversity. The problem is one of incentive. Does anyone really care about the ancestors of the beloved apple?

The imminent death of the Cavendish banana

Given that humans acquired the knowledge and technology to genetically modify organisms which enables us to increase the fitness of a (critically) endangered species, do we have the moral right to do so?

This scenario really highlights a moral paradox .. On face value both deontic or utilitarians could technically come to this sort of conclusion -- on animal rights ground it's important to reduce unnecessary suffering and death; on 'good' maximization grounds its important to maximize longevity/livelihood of animals. But effects of applying this sort of thing may, in the long run reduce fitness of animals via minimizing species diversity. This is in effect circumventing of selection constraints.

the fitness of a (critically) endangered species — Hans

The fitness of critically endangered megafauna is in good shape. There is no improved fitness possible for various megafauna if we decide to kill all of them for their tusk, tail, testicles, or whatever. Maybe somebody could modify the white rhino so that it could shoot to kill in self-defense?

As for modifying the genes of various non-glamorous non-megafauna, we don't know what conditions they should be able to survive (because global warming is changing so many environments so rapidly). At the rate we're going, WE won't be around long enough to carry out much genetic jiggering.