The virtual meeting comes after North Korea earlier this week suggested it might resume nuclear and long-range missile testing that has been paused for more than three years.
Kishida also named stepping up defence measures against rising regional threats as a priority, hours after North Korea test-fired two possible ballistic missiles, it's fourth this year.
Japan briefly eased border controls in November after COVID-19 cases rapidly declined, but quickly reinstated a ban on most foreign entrants after the highly transmissible new variant emerged.
South Korea’s Joint Chiefs of Staff said North Korea likely fired a single ballistic missile from an inland area to its eastern sea.
Prime Ministers of both nations met in a virtual summit to sign the Reciprocal Access Agreement, the first such defence pact signed by Japan with any country other than the United States.
In September, Australia signed the so-called Aukus trilateral security pact with the US and Britain under which those two countries pledged to help Australia acquire nuclear-powered submarines.
Japan has confirmed a handful of omicron variant cases, while revealing a cluster of infections of about 100 U.S. troops on Japan's southern island of Okinawa since earlier this month.
The prime piece of real estate in central Tokyo stood empty during the terms of Kishida's most recent predecessors, Yoshihide Suga and Shinzo Abe.
Visits and donations to the Yasukuni shrine by Japanese political leaders are seen by critics as a sign of a lack of remorse over the country’s wartime actions.
The decision means Japan will restore border controls that it eased earlier this month for short-term business visitors, foreign students and workers.
Fumio Kishida, who took office in October, served as top commander for the first time at Saturday's Self-Defense Force troop review held at the main army base Camp Asaka, north of Tokyo.
The plan includes doling out 100,000 yen ($880) each in monetary assistance to those 18 years or younger, and aid for ailing businesses, Kishida and other politicians said.
Fumio Kishida’s immediate post-election task is to compile a major economic stimulus package of about 30 trillion yen ($265 billion) that includes cash payouts, to be announced next week.
Kishida told reporters later in the day he agreed with Biden to meet again at the earliest date possible, which could be later this year, to have more 'thorough' discussions.
Kishida’s Liberal Democratic Party and its junior coalition partner Komeito together were expected to win between 239 to 288 seats in the 465-member lower house.