|Covid-19|January – Pope Alexander IV prohibits the Flagellants.
March 13 – Treaty of Nymphaeum between the Republic of Genoa and the Nicaean emperor Michael VIII Palaiologos, directed against the Latin Empire of Constantinople.
June 12 – King Henry III of England obtains a papal bull releasing him from his oath to maintain the Provisions of Oxford, setting the stage for the Second Barons' War (1263–1267).
July 4 – Baybars becomes the new Mamluk Sultan of Egypt.
July 23 – At the Battle of Callann, the Normans, under John FitzGerald, 1st Baron Desmond, are defeated by the Gaelic forces of Fínghin Mac Carthaigh, King of Desmond.
July 25 – The city of Constantinople is recaptured by Nicaean forces under the command of Alexios Strategopoulos, thus ending the Latin Empire and re-establishing the Byzantine Empire.
August 15 – The Nicaean ruler Michael VIII Palaiologos is crowned Byzantine emperor in Constantinople.
August 29 – Pope Urban IV succeeds Pope Alexander IV as the 182nd pope, the last man to do so without being a cardinal first.
December 25 – The 11-year-old John IV Laskaris is blinded by order of his cousin and nominal co-ruler of the Byzantine Empire, Michael VIII Palaiologos, in Nicaea to render him ineligible for the throne and he is exiled.
The population of Greenland accepts the overlordship of the King of Norway.
Livonian Crusade: The Estonian rebellion on Saaremaa Island is forced down by the Livonian Order.
The Japanese Bun'ō era ends, and the Kōchō era begins.
The Convent of Wurmsbach is established in Switzerland.
Baibars establishes a puppet caliphate in Cairo.
Béla IV of Hungary repels a Tatar invasion.
Kublai Khan, who became a Khagan claimant in the previously year, releases 75 Song Dynasty Chinese merchants from captivity after they had been captured along the border of his Empire and the Southern Song Dynasty of China. This is an act to increase his reputation amongst the Chinese, shore up his legitimacy as a just ruler, and to gain more defectors from the Southern Song Dynasty.
The earliest extant Chinese illustration of 'Pascal's triangle' is from Yang Hui's book Xiangjie Jiuzhang Suanfa, published in this year, although knowledge of Pascal's Triangle existed in China by at least 1100.
February 1 – Walter de Stapledon, English bishop (d. 1326)
February 11 – Otto III, Duke of Bavaria (d. 1312)
July 25 – Arthur II, Duke of Brittany (d. 1312)
October 9 – King Denis of Portugal (d. 1325)
Bohemond VII, Count of Tripoli, prince of Antioch (d. 1287)
Prince Daniel of Moscow, son of Alexander Nevsky (d. 1303)
Konoe Iemoto, Japanese kugyō (d. 1296)
Albertino Mussato, statesman and writer (d. 1329)
Władysław I the Elbow-high, King of Poland (d. 1333)
Constantine Palaiologos, Byzantine prince and general (d. 1306)
February 28 – Henry III, Duke of Brabant
May 25 – Pope Alexander IV
July 8 – Adolf IV of Holstein, Count of Schauenburg
September – Plaisance of Antioch, queen of Cyprus
September 18 – Konrad von Hochstaden, Archbishop of Cologne
November 9 – Sanchia of Provence, queen consort of Germany
An-Nasir Dawud, Ayyubid sultan of Damascus and Emir of Kerak
Bettisia Gozzadini, scholar (b. 1209)
Qin Jiushao, Chinese mathematician of the Song Dynasty (b. 1202)
Patriarch Nicephorus II of Constantinople
Year 1261 (MCCLXI) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.