BEIJING -- Some countries and organizations have extended condolences to China over a deadly earthquake which jolted China's southwestern province of Yunnan on Sunday, and had left nearly 400 people dead.

Russian President Vladimir Putin has expressed his condolences to Chinese President Xi Jinping in the wake of the earthquake, the Kremlin said Monday.

Live:398 dead as strong quake jolts SW China

Putin "expressed his words of sympathy and support to friends and relatives of those killed and wished soonest recovery to all injured," the Kremlin press service said in a statement.

He also expressed readiness to provide disaster relief assistance "if the need arises," added the statement.

Meanwhile, Russian Prime Minister Dmitry Medvedev also conveyed a message of condolence to Chinese Premier Li Keqiang over the earthquake.

UN Secretary-General Ban Ki-moon said on Sunday in New York that he "is saddened by the loss of life, and the damage to homes and infrastructure" in the earthquake.

The UN chief "offers his condolences to the Chinese government and the families of those killed, and his deepest sympathies to those who were injured or otherwise affected in this disaster," said a statement issued by Ban's spokesman.

"The United Nations stands ready to lend its assistance to efforts to respond to humanitarian needs created by the disaster and to mobilize any international support needed," it said.

Kazakh President Nursultan Nazarbayev, in a message sent to Chinese President Xi on Monday, expressed sympathy to the relatives of the quake victims. He wished that the Chinese people will turn grief into strength and believed that the losses caused by the natural disaster could be recovered soon.

Kyrgyz President Almazbek Atambayev also extended his condolences to the Chinese people following Sunday's earthquake.

Noting that the quake left many people dead as well as significant destruction, Atambayev said on Monday he hoped the wounded can recover soon.

In a message sent to her Chinese counterpart Xi on Sunday, South Korean President Park Geun-hye expressed deep grief over the significant casualties and properties losses caused by the earthquake, wishing China will win the disaster-relief battle soon.

Japanese Prime Minister Shinzo Abe offered condolences to Chinese President Xi and Premier Li on Monday over the deadly quake, expressing "heartfelt sympathy and condolences" to the government and people of China. He said Japan is ready to extend support to help China cope with the aftermath of the quake.

Japanese Foreign Minister Fumio Kishida conveyed a similar message to Chinese Foreign Minister Wang Yi, according to the Japanese Foreign Ministry.

The White House on Sunday offered condolences over loss of lives in the strong earthquake, saying the United States was ready to help.

"The United States offers sincere condolences to all those who lost loved ones in the Aug. 3 earthquake in southwestern China," National Security Council spokeswoman Bernadette Meehan said in a statement.

"Our thoughts and prayers are with the families of those that lost their lives, those injured or displaced, and all the people of China on this difficult day," she added.

The Mexican Foreign Ministry, in a statement issued on Sunday, said the Mexican government extended condolences to the Chinese government and people over the strong earthquake in Yunnan, southwestern China.

Mexico is willing to cope with the earthquake together with China, and offer full cooperation and humanitarian assistance, if China needs, the statement said.

A 6.5-magnitude earthquake jolted Zhaotong City in southwest China's Yunnan Provinceon Sunday. According to the latest official statistics, the death toll had risen to 398, while more than 1,800 people were injured.