SEOUL (Reuters) - About 500 United States and South Korean marines began small-scale military drills on Monday, just days before U.S. Secretary of State Mike Pompeo is set to hold talks with North Korea on denuclearization and plans for a second summit of their leaders.

The Korean Marine Exchange Program was among the training drills indefinitely suspended in June after U.S. President Donald Trump met North Korean leader Kim Jong Un in Singapore and promised to end joint, U.S.-South Korea military exercises.

Although larger exercises were suspended, the two countries have continued small-scale drills, the South’s Ministry of National Defense said on Monday, adding that the marines were holding a training round near the southern city of Pohang.

Pompeo, interviewed on broadcaster CBS’s “Face the Nation,” said on Sunday he would be in New York City at the end of this week to meet his North Korean counterpart, Kim Yong Chol.

“I expect we’ll make some real progress, including an effort to make sure that the summit between our two leaders can take place, where we can make substantial steps towards denuclearization,” he added.

In Washington last week, South Korea’s defence minister said the two countries would decide by December on major joint military exercises for 2019. Vigilant Ace, suspended this month, is one of several such exercises halted to encourage dialogue with Pyongyang, which has criticised joint U.S.-South Korea exercises in the past.

The biggest combat-readiness war game ever staged in and around Japan has gone ahead, however, with nuclear-powered aircraft carrier USS Ronald Reagan joining Japanese destroyers and a Canadian warship in the ocean off Japan, another key player in the effort to pressure North Korea.

FILE PHOTO: South Korean marines march during a military exercise as a part of the annual joint military training called Foal Eagle between South Korea and the U.S. in Pohang, South Korea, April 5, 2018. REUTERS/Kim Hong-Ji/File Photo

This week’s exercises follow a warning by North Korea on Friday that it could resume development of its nuclear programme if the United States did not drop its campaign of “maximum pressure” and sanctions.

“The improvement of relations and sanctions are incompatible,” a foreign ministry official said in a statement released through state-run KCNA news agency.

“The U.S. thinks that its oft-repeated ‘sanctions and pressure’ lead to ‘denuclearization.’ We cannot help laughing at such a foolish idea.”

South Korea hopes the North and the United States will make “big progress” during the talks set for this week, presidential spokesman Kim Eui-kyeom said on Monday, but declined to comment on the North’s Friday statement.

North Korea has not tested a ballistic missile or nuclear weapon for nearly a year, and has said it has shuttered its main nuclear test site with plans to dismantle several more facilities.

In recent weeks, North Korea has pressed harder for what it sees as reciprocal concessions by the United States and other countries.

“As shown, the U.S. is totally to blame for all the problems on the Korean peninsula, including the nuclear issue and therefore, the very one that caused all those must untie the knot it made,” it said on Friday.

American officials have remained sceptical of Kim’s commitment to give up his nuclear arsenal, however, and Washington says it will not support easing international sanctions until more verified progress is made.

Pompeo, interviewed on television’s “Fox News Sunday,” said the Trump administration wants a full, verifiable denuclearization of the Korean peninsula, adding that Trump insisted on “no economic relief until we have achieved our ultimate objective.”

South Korean President Moon Jae-in’s continuing efforts to engage with North Korea have fanned U.S. concerns that Seoul could weaken pressure on North Korea to give up nuclear weapons.