They made the remarks during a luncheon hosted by Kim on Friday, the last day of Xi's two-day state visit to Pyongyang during which the leaders highlighted their traditional alliance amid tensions with the United States over China's trade practices and the North's denuclearization.
"Kim Jong-un and Xi Jinping referred to the fact that through the five rounds of meetings in a little more than a year they had profound communications as well as excellent and beneficial talks to have deep understanding of each other," the North's official Korean Central News Agency (KCNA) reported.
"(They) reached a consensus on important issues, deepened the comradely trust and forged special relations of friendship, and expressed their will to creditably carry forward and glorify the friendly relations between the two parties and the two countries in the future, too, whatever the international situation," it added.
Also present at the luncheon were Xi's wife, Peng Liyuan, and Kim's wife, Ri Sol-ju. The leaders and their wives walked together in a garden of the Chinese leader's lodging in Pyongyang to deepen their friendship in a "harmonious atmosphere," according to the report.
In a separate article, the state media also reported on Kim seeing off Xi at an airport in the North's capital.
"The top leaders of the two countries respectively exchanged farewell with the officials of each other's side," KCNA said.
"Kim Jong-un and Xi Jinping exchanged firm handshake of farewell, promising to steadily bring about efflorescence and development of the DPRK-China friendship of the great new era in line with the wishes of the two parties and two peoples," it added.
DPRK stands for the North's official name, the Democratic People's Republic of Korea.
According to a report by China's Xinhua News Agency, Song Tao, head of the International Liaison Department of the Central Committee of China's Communist Party, said that the leaders have reached a "key consensus" on writing new chapters for their countries' friendship and safeguarding peace and stability on the peninsula.
"Xi's visit was a visit of friendship and peace, and has displayed China's determination to stay committed to consolidating the traditional China-DPRK friendship, supporting the implementation of DPRK's new strategic line and promoting a political solution to solving the nuclear issue in the peninsula,"
Xinhua quoted Song as saying.
He was apparently referring to Kim's new policy line of focusing on economic development.
The report also emphasized that Xi's trip injected "new vitality" into the political dialogue on the peninsula issue.
It was Xi's first trip to the North since taking power in 2013 and the first by a Chinese head of state in 14 years.
Xi is expected to share the outcome of his talks with Kim during his planned summit with U.S. President Donald Trump on the sidelines of the Group of 20 summit in Osaka, Japan, on June 28 and 29. (Yonhap)