The He 111P incorporated the updated Daimler Benz DB601A-1 water-cooled engine and featured a newly designed nose section, including an asymmetric Ikaria nose mounting for an MG 15 machine gun that replaced the 'stepped' cockpit with a roomier and aerodynamically favourable, heavily glazed stepless cockpit over the front of the aircraft, a feature to be widely adopted - with some variations - on many German twin and multi-engined military airframe designs to come. This new "bullet" smooth glazed nose was first tested out on the He 111 V8 in January 1938. These improvements allowed the aircraft to reach 475 km/h (295 mph) at 5,000 m (16,400 ft) and a cruise speed of 370 km/h (230 mph), although a full bombload reduced this figure to 300 km/h (190 mph). The design was implemented in 1937 because pilot reports indicated problems with visibility. The pilot's seat could actually be elevated, with the pilot's eyes above the level of the upper glazing, complete with a small pivoted windscreen panel, to get the pilot's head above the level of the top of the "glass tunnel" for a better forward view for takeoffs and landings.

One of Heinkel's rivals, Junkers, built 40 He 111Ps at Dessau. On 8 October 1938, the Junkers Central Administration commented:

Two aircraft were able to be inspected on 6th October in Bernburg. Apparent are the externally poor, less carefully designed components at various locations, especially at the junction between the empennage and the rear fuselage. All parts have an impression of being very weak; especially when one is used to taking a long look at Junkers' designs, one cannot dispel a feeling of uncertainty. The visible flexing in the wing must also be very high. The left and right powerplants are interchangeable. Each motor has an exhaust-gas heater on one side, but it is not connected to the fuselage since it is probable that as a result of incorrect air feed, the warm air in the fuselage is not free of carbon monoxide(CO). The fuselage is not subdivided into individual segments, but is attached over its entire length, after completion, to the wing centre section. Outboard of the powerplants, the wings are attached by universal joints. The latter can in no way be satisfactory and have been the cause of several failures.

The new design was powered by the DB 601 Ba engine with 1,175 PS and reduced the length of the aircraft by 1.1 m (3.6 ft). The He 111P's DB601 powerplant exhaust pipes had a second outlet on the top of the engine which pumped hot air back into the aircraft to warm crews. It was designated as P-0, and the first production lines reached their units in Fall 1938. In May 1939, the P-1 and P-2 went into service with improved radio equipment. The P-1 variant was produced with two DB 601Aa powerplants of 1,150 hp (860 kW). The fuel tanks had the added innovation of self-sealing fuel tanks to protect them from enemy fire. The Nose department itself was now fully glazed and the "stepped up" cockpit was dispensed with. The P-1 was powered by a DB 601Aa engine and given a semi-retractable tail wheel to decrease drag. Armament consisted of a MG 15 mounted in the Ikaria A Stand mount in the nose, and a sliding hood for the fuselage's dorsal B-Stand position. Installation of upgraded FuG III radio communication devices were also made and a new ESAC-250/III vertical bomb magazine was added. The overall takeoff weight was now 13,300 kg (29,321 lb).

The P-2, like the later P-4, was given stronger armour and two MG 15 machine guns in "waist" mounts on either side of the fuselage and two external bomb racks. Radio communications consisted of FuG IIIaU radios and the DB601 A-1 replaced the 601Aa powerplants. The Lotfernrohr 7 bombsights, which became the standard bombsight for German bombers, were also fitted to the P-2. The P-2 was also given "field equipment sets", to upgrade the weak defensive armament to four or five MG 15 machine guns. The P-2 had its bomb capacity raised to 4 ESA-250/IX vertical magazines. The P-2 thus had an empty weight of 6,202 kg (13,272 lb), a loaded weight increased to 12,570 kg (27,712 lb) and a maximum range of 2,100 km (1,305 mi).

The P-3 was powered with the same DB601A-1 engines. The aircraft was also designed to take off with a land catapult (KL-12). A towing hook was added to the fuselage under the cockpit for the cable. Just eight examples were produced, all without bomb equipment. The P-4 contained many changes from the P-2 and P-3. The jettisonable loads were capable of considerable variation. Two external SC 1800 kg (3,960 lb) bombs; two LMA air-dropped anti-shipping mines; one SC 1,800 kg plus four SC 250 kg; or one SC 2,500 kg external bomb could be carried on an ETC Rüstsatz rack. Depending on the load variation, a 835 L fuel and 120 L oil tank could be added in place of the internal bomb bay. The armament consisted of three defensive MG 15 machine guns. But these were not sufficient, so a further three MG 15s and one MG 17 machine gun was added. The radio communications were standard FuG X(10), Peil G V direction finding and FuBI radio devices. Because of the increase in defensive firepower, the crew numbers increased from four to five. The empty weight of the P-4 increased to 6,775 kg (14,936 lb), and the full takeoff weight increased to 13,500 kg (29,762 lb) owing to the mentioned alterations. The P-5 was powered by the DB601A. The variant was mostly used as a trainer and at least 24 production variants were produced before production ceased. The P-5 was alleged to have been fitted with PVC bomb racks, which cannot be confirmed. The P-5 was fitted with meteorological equipment, and was used in Luftwaffe weather units. Many of the He 111 Ps served during the Polish Campaign. With the Junckers Ju-88 experiencing technical difficulties, the He 111 and the Do 17 formed the backbone of the Kampfwaffe. On 1 September 1939, Luftwaffe records indicate the Heinkel strength at 705 (along with 533 Dorniers).

The P-6 variant was the last production model of the He 111 P series. In 1940, the Ministry of Aviation abandoned further production of the P series in favour of the H versions, mostly because the P-series' Daimler-Benz engines were sorely needed for Messerschmitt Bf 109 and Bf 110 fighter production. The remaining P-6s were redesignated P-6/R2s and used as heavy glider tugs. The most notable difference with previous variants was the upgraded DB 601N powerplants.

The P-7 variant's history is unclear. German archives do not produce any reliable information for this variant, if it existed. The P-8 was said to have been similar to the H-5 fitted with dual controls. Its existence cannot be established. The P-9 was produced as an export variant for the Hungarian air force. Due to the lack of DB 601E engines, the line was terminated in Summer 1940.^[

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