China and Russia have started joint naval drills in the waters near the Russia-North Korea border, local media reported.

The exercises, which began on Monday off Russia's southeastern port of Vladivostok, are the second part of China and Russia's 'Joint Sea-2017' programme that started in June.

The drills, which include submarine rescue and anti-submarine exercises, are not directly linked to increasing tensions over North Korea, China's state-owned Xinhua news agency reported.

The exercises are taking place in the Sea of Japan and, for the first time, the Okhotsk Sea.

South Korea and the United States also staged military drills in the Korean Peninsula on Monday, conducting bombing exercises involving six US planes and four South Korean fighter jets, according to Song Young-moo, the South Korean defence minister.

Joint drills organised by Washington and Seoul are now being conducted "two to three times a month these days", he said.

READ MORE: North Korea tensions - All the latest updates

Tensions have been rising on the Korean Peninsula in recent weeks, following North Korea's sixth, and most powerful, nuclear test to date on September 3.

The UN Security Council (UNSC) voted unanimously to impose fresh sanctions on North Korea last week after a meeting on September 11 in response to the crisis.

Pyongyang has claimed the measures - including a ban on textiles and a cap on oil supplies - will speed up North Korea's nuclear weapons programme.

"The increased moves of the US and its vassal forces to impose sanctions and pressure on the DPRK will only increase our pace towards the ultimate completion of the state nuclear force," a statement on North Korean state media said on Monday, using the acronym for the country's official name, the Democratic People's Republic of Korea.

READ MORE: N Korea says sanctions will speed up nuclear programme

China and Russia have repeatedly called for a peaceful solution to the crisis.

However, Nikki Haley, the US ambassador to the UN, claimed the UNSC has now run out of options and has warned the matter may now need to be turned over to the Pentagon.

"We have pretty much exhausted all the things that we can do at the Security Council at this point… We're trying every other possibility that we have, but there's a whole lot of military options on the table," she told CNN on Sunday.

Kim Jong-un, the North Korean leader, claims Pyongyang needs a nuclear weapons programme to deter the US from invading the isolated state.

The US and South Korea are technically still at war with North Korea because the 1950-53 Korean conflict ended with a truce and not a peace treaty.