It's the first time Abe has put a clear time frame on revising the constitution, which contains language that bans Japan from maintaining armed forces.
The Japanese military is known as the Self-Defense Forces, but Abe said there is a contradiction between the constitution and the existence of the SDF.
"I believe that we must establish the status of the SDF explicitly in the constitution during our generation's lifetime and leave no room for contending the SDF could be unconstitutional," Abe said in a video message to a Tokyo forum marking the 70th anniversary of the constitution. "I strongly wish to make 2020 the year that the reborn Japan will make a new start."
Japan's current constitution came into effect in 1947 after its defeat by allied forces in World War II. Article 9 of the document says that "land, sea and air forces, as well as other war potential will never be maintained."
Abe's proposed changes are essentially symbolic, said Corey Wallace, a Japan security expert at Freie University in Berlin.
"It would be a cosmetic change in terms of actual implications for Japan's defense posture," he said.
But changing the constitution "could symbolically represent a Japan that is willing to adapt to developments around it and not burdened by the past," Wallace told CNN.
"Pilot for pilot, ship for ship, Japan can stand toe to toe with anybody," John T. Kuehn, a professor of military history at the US Army Command and General Staff College, told CNN last year.
North Korean threat
Abe's comments come at a time when Japan's forces are increasingly in the spotlight as they participate in exercises with the United States and other allies in response to North Korean threats.
Recent North Korean missile tests have landed in the waters off Japan, and in March state-run Korean Central News Agency said units conducting the drills were "tasked to strike the bases of the US imperialist aggressor forces in Japan."
This week, Japan's largest warship, the helicopter carrier Izumo, escorted a US naval supply ship that could be used to refuel US Navy warships operating with the Vinson, according to Japanese media
And last month, Abe said Japan could become a target for North Korean missiles
carrying warheads filled with sarin gas.
"The security situation around our country is getting increasingly severe," Abe said in mid-April, referring to the North Korean threat.
But analysts say Japan is in a good position to deal with any potential attack from Pyongyang.
The pacifist constitution has helped make its military as formidable as it is because to this point it has only had to concentrate on defensive operations, they say.
But they add the current situation in north Asia has exposed a weakness -- Japan lacks some of the hardware necessary for it to counterattack alone if North Korean missiles were to strike.
"They can bomb anyone landing on one of Japan's main islands ... but they can't strike Chinese or North Korean air bases or missile sites," said Carl Schuster, a former director of operations at the US Pacific Command's Joint Intelligence Center.
Schuster points out that Japanese warplanes don't carry the equipment necessary to suppress enemy air defenses. "They can defend, but they can't punch back," he said.
Before the constitution can be amended, the revision must be proposed by two-thirds of the members of each chamber of Japan's parliament and must be approved by a majority of voters in a referendum.