If we could loosen the definition of what constitutes the Ottoman Empire, we could perhaps examine the various adventures of Egypt (and Sudan) during this period. The pashas that ruled Egypt were, nominally speaking, doing so on behalf of the Ottoman Empire (their title was wali or viceroy) though their ambitions and capabilities were often greater than that of mere provincial governors and they acted quite independently from their supposed overlords in Anatolia.

The pasha that ruled Egypt during most of the American Civil War was Said Pasha (1855-1864). Said Pasha could be described as pro-French (which will become relevant further on) but also adopted a pro-Union stance. He closed his ports to Confederate shipping and attempted to broker a sale for 47,000 Minie rifles to the Union though this sale fell through. The American Civil War also provided quite a windfall for the Egyptian cotton industry as it greatly disrupted the production of a major competitor and sent the prices of Egyptian cotton skyrocketing by 1200 percent!

Egypt also had a minor but crucial role in one of the strangest episodes in this period - the French invasion of Mexico. In 1861, the Mexican government had imposed of a moratorium on international debt payments. The French emperor, Napoleon III used this as a pretext to invade in 1862 and install a puppet monarchy in Mexico. This invasion was a violation of the Monroe Doctrine however due to the ongoing Civil War, the United States could do little but withhold recognition of the French puppet state. The Confederacy was more favorable to this invasion and hoped for potential military and commercial cooperation with this new regime (and by extension France; this did not pan out and the new ruler of Mexico, Archduke Maximilian refused to meet with the Confederate envoy). The Egyptians were called by Napoleon III to contribute a 1200 to 1500 black soldiers to the invasion force. These troops were to hold the key port of Vera Cruz and guard the route to Mexico City. They were requested due to their resistance to the numerous tropical diseases that proliferated in the swamps and lagoons surrounding the port. Ultimately only 450 troops drawn from Sudan were sent on this Mexican adventure and these troops acquitted themselves quite well, earning 67 decorations over the course of 4 years of combat (the French intervention concluded in 1867 with the withdrawal of French forces from Mexico).

Sources: John Dunn. Africa Invades the New World: Egypt’s Mexican Adventure, 1863–1867. War in History.

John Dunn. Egypt‘s Nineteenth Century Armament‘s Industry. Girding for Battle: The Arms Trade in a Global Perspective, 1815-1940

Don M. Coerver. Mexico: Conflicting Self-Interests. United States-Latin American Relations, 1850-1903: Establishing a Relationship.

The Ottoman Empire generally favored the Union side in the war, sending observers to the fighting on the Union side and favoring the Union in diplomacy and trade. In 1862, for example, the U.S. concluded a trade treaty with the Ottoman Empire, and in return Sultan Abdulaziz issued a proclamation forbidding privateers from entering Ottoman waters and ports.

This was a big deal because Confederate raiders were the biggest single international issue pertaining to the war. Ships like the Alabama and Florida took a huge toll on American shipping, and the raiders took advantage of neutrality rules to resupply at ports like Cape Town.

The Ottoman government also sent messages of congratulations to the federal government after significant victories, and after the war was concluded, it bought significant amounts of surplus weapons left over from the war. Suhnaz Yilmaz's Turkish-American Relations, 1800-1952 mentions these issues in passing.

It's also important to understand that the Ottoman Empire benefitted from the war in that the Union blockade of the South meant that Southern cotton was no longer available to European and American mills. This led to a surge in Egyptian cotton, which benefitted the Empire.

Like every other major European power, the Ottoman Empire sent observers to study the war. One of the most prominent was Major Gen. Charles F. Havelock of the Imperial Ottoman Army. If that sounds like a strange name for an Ottoman soldier, it is.

During the 19th century, militaries tended to borrow officers from noncombatant countries with some regularity.

In this case, Charles Frederick Havelock was born in England and commissioned into the British Army in 1821, fighting in India and Afghanistan. He joined the Ottoman Irregular Cavalry and in 1856 was promoted to major general (the Ottomans, favoring British expertise, had promoted the man much more than the British Army did).

In 1861, he came to the United States, ostensibly to observe the fighting for the Ottomans. He was accompanied (according to an article in Frank Leslie's Illustrated Newspaper) by the Count de Sayre and the Baron de Schonen.

Havelock wasn't content to sit on the sidelines, however, and after First Bull Run, he volunteered to join the Union Army. Lincoln appointed him a colonel, a rank that was confirmed by Congress in November, and he became aide-de-camp to Maj. Gen. George McClellan.

A letter pertaining to Havelock's service (which was abbreviated in 1863), recently came up for auction, and you can see it here.