In May 2013 Parmitano partnered with his 15-year-old mentee Abigail Harrison to have her serve as his Earth liaison during his mission on Expedition 36 and Expedition 37. Harrison shared Parmitano's experience of living in space on the International Space Station with her online community on social media and her blog, where she is known as "Astronaut Abby".
On 9 July 2013, he became the first Italian to take part in a spacewalk as he and Chris Cassidy conducted an EVA out of the ISS' quest airlock to install power cables, retrieve material research samples (MISSE-8) and accomplish a number of maintenance tasks. During the EVA, Parmitano also got to ride on the ISS' Mobile Servicing System for the installation of a couple of radiator grapple bars previously flown up on SpaceX' CRS-2 mission. The EVA was part of preparations for the new Russian multipurpose module planned to replace the Pirs docking compartment by the end of 2013. In 2013, AOL's BermanBraun listed his space selfie taken during this spacewalk as one of the 50 best space photos of the year.
His second EVA on July 16, 2013 was terminated after only 1 hour and 32 minutes, when the helmet of his Extravehicular Mobility Unit suit started filling with water. Water in his helmet posed the danger of drowning and made his return to the airlock even more difficult, as orbital sunset had occurred just before he started to return. Engineers found that contamination had clogged one of the suit's filters, causing water from the suit's cooling system to back up. On 15 January 2016, astronaut Timothy Kopra experienced a water leak in the same spacesuit. Parmitano returned to Earth on 11 November 2013 aboard Soyuz TMA-09M.