Yes, numerous Precolumbian civilizations had writing in various forms, though only one has been (or probably will ever be) deciphered, and every single example comes from Mesoamerica, which is in Mexico (thus North America).

The earliest examples of writing in Mesoamerica come from the Olmecs, Zapotecs, and Maya and examples have been found around the Isthmus of Tehuantepec for the Olmecs, Monte Alban for the Zapotecs, and across the entire Maya Area for the Maya.

The earliest examples of the Maya Script have been found in San Bartolo in Central Guatemala, and have been dated to around 300 BCE. Most Maya inscriptions are known from the Classic Period (250 CE - 900 CE) from big sites like Palenque, Tikal, Calakmul, Copan, etc. There are countless examples of the Maya Script, though most of them take the form of inscriptions on stelae that tell of the deeds of elites. Therefore, they are history, not literature, though they were often used for propaganda. There are also a few surviving examples of Mayan books, such as the Dresden Codex, which are usually almanacs containing astronomical data. None of these books survive from the Classic (they would have degraded), though many are assumed to contain information that goes back that far. Unfortunately the early Spanish colonizers intentionally destroyed all of the Prehispanic texts they could, but luckily a few survived. The Maya Script was still being taught and used by scribes and priests after the Conquest, and due to this one of the priests who was in charge of burning Mayan texts managed to create a sort of Rosetta Stone (the confusing De Landa Alphabet) that the Russian Mayanist Yuri Knorozov finally managed to figure out in the 50's in order to decipher the Maya Script. This is a long story that's sort of beside the point, but if you're interested in it I recommend reading Breaking the Maya Code by Michael D. Coe.

The Maya Script was logosyllabic, which means it employs symbols that both represent concepts directly (usually radicals or determiners) as well as phonetic signs that represent syllables. These are structurally the same as Egyptian Heiroglyphs, Chinese Characters, and Sumerian Cuneiform, and due to this it's suggested that early scripts tend to form in this way before diversifying into different forms (if they ever do that). Much like Egyptian Heiroglyphs, there were numerous glyphs that could be used to represent the same sounds or set concepts depending on how they were used. For example, a symbol of a jaguar's head could have been used to represent the idea of a jaguar, or it could have been used via the rebus principle to represent part, or all of the sounds of the Classic Maya word for jaguar (balaam). This flexibility made the script very complex due to its preponderance of symbols, but allowed for tremendous artistic expression when the scribe wanted to express their creativity and skill. The Maya Script is about 99% fully deciphered at this point, and all texts are readable to a high degree of accuracy.

Examples of the so-called Isthmian script from the Epi-Olmec culture are found on various pieces of artwork such as the La Mojarra Stele, Tres Zapotes Stele C, the Tuxtla Statuette, and some other pieces. These date to around the same time as the earliest Mayan inscriptions, and are all the same script, though it is not known what language it represents (or if it even represents one language). The script superficially resembles the Maya Script, and while that is deciphered, this one will likely never be unless a bilingual text or "Rosetta Stone" (like the De Landa Alphabet) is discovered (which is extremely unlikely). Despite this, the form it takes implies it's likely logosyllabic like the Maya Script.

The Zapotec Script appears on inscriptions at the monumental site Monte Alban, often on inscriptions representing captives (the so-called Danzantes). Due to its form, this script is often considered more ideographic and less phonetic than the Maya and Isthmian scripts. It seems to resemble the later symbolic systems of Central Mexico to a much greater degree. These scripts used set glyphs to represent proper nouns as labels, and could have been used to notate tribute lists and maps that described territorial control. There is evidence that these scripts could have been more flexible than this, and by applying the rebus principle (the same way the Maya Script did), could apply their symbols to other things as syllables in a more phonetic sense. If this is the case, it doesn't seem to have been standardized to the same degree as the Maya Script. Like the Isthmian script, it will never be deciphered, though it is thought to have represented an early Zapotec language. Later scripts of this form, such as that of the Aztecs, are understood to a much greater degree, and glyphs representing proper nouns were recorded by Spaniards.

I haven't mentioned Prehispanic literature yet, but it does exist. The Popol Vuh is a famous text that was actually recorded after the Conquest, but is known by historians to have existed in various forms for millenia. The text describes the Mayan creation myth, stories about the Hero Twins Hunahpu and Xbalanque, and other stories depending on the version. It's known that these stories go back millenia because there are artistic representations of them going back as far as the proto-Mayan site of Izapa. This stele, for example, shows the Hero Twins hunting the Principle Bird Deity, an important story from the Popol Vuh. Here are some other examples of the Hero Twins from various Maya cultures depicted over many centuries.