SEOUL (Reuters) - The two Koreas agreed on Monday to begin reconnecting rail and road links, another step in an improving relationship in spite of U.S. concerns that the rapid North-South thaw could undermine efforts to press North Korea to give up its nuclear weapons.

FILE PHOTO: Head of the North Korean delegation, Ri Son Gwon shakes hands with South Korean counterpart Cho Myoung-gyon as they exchange documents after their meeting at the truce village of Panmunjom in the demilitarised zone separating the two Koreas, South Korea, January 9, 2018. REUTERS/Korea Pool/File Photo

The agreement on transport links came during talks in the border village of Panmunjom aimed at following up on the third summit this year between South Korea’s President Moon Jae-in and North Korean leader Kim Jong Un, last month.

“The South and North reached the agreement after sincerely discussing action plans to develop inter-Korean relations to a new, higher stage,” said a joint statement released by the South’s Unification Ministry.

The two sides agreed to hold ceremonies in late November or early December to inaugurate work on reconnecting railways and roads that have been cut since the 1950-53 Korean War.

They will carry out joint field studies on the transport plans from late this month, the statement said.

They also agreed to discuss late this month a plan to pursue a bid to co-host the 2032 Olympic Games, and to explore in November ways to restart webcam reunions and video exchanges for families separated by the Korean War.

Military officials from both sides are to meet “in the near future” to craft follow-on steps to a military pact struck at last month’s summit.

That accord includes the reinstatement of a joint military commission, the halting of military exercises, a no-fly zone near their border and the gradual removal of landmines and guard posts within the Demilitarized Zone (DMZ).

Meetings will also be held on reforestation on Oct. 22, and on health and disease prevention in late October at a joint liaison office opened last month in the North’s border city of Kaesong.

The talks were led by the South’s Unification Minister Cho Myoung-gyon and Ri Son Gwon, chairman of the North’s committee for peaceful reunification that handles cross-border affairs.

“We are at a very critical moment for the denuclearization of the Korean peninsula and the advancement of inter-Korean relations, and there’s also a second North Korea-U.S. summit coming up,” Cho told reporters before leaving for Panmunjom.

While the two Koreas have moved ahead in the rapprochement, Washington has been more cautious than its ally Seoul in spite of an unprecedented summit between U.S. President Donald Trump and Kim in June and plans for a second meeting.

Washington says sanctions must remain in place until North Korea gives up its nuclear weapons and is concerned that the North-South thaw may be outpacing practical progress in denuclearization.

In a rare confirmation of discord between Seoul and Washington, South Korea’s foreign minister Kang Kyung-wha said last week that U.S. Secretary of State Mike Pompeo had expressed “discontent” over the inter-Korean military agreement.

In August, a joint inspection plan for the rail project was scrapped after the U.S.-led United Nations Command (UNC), which oversees affairs in the DMZ, refused passage for a test train, military sources said.

On Monday a spokeswoman for the U.S. State Department said Moon had stated in the past that “improvement of relations between North and South Korea cannot advance separately from resolving North Korea’s nuclear program.”

“We expect all member states to fully implement U.N. sanctions, including sectoral goods banned under U.N. Security Council resolutions, and expect all nations to take their responsibilities seriously to help end (North Korea’s) illegal nuclear and missile programs,” she added.

In final remarks on Monday, North Korea struck a sour note, with Ri blaming Seoul for hurdles in implementing their pacts.

“If we look back at the projects we have been carrying out so far, there are problems that should be fixed, and the South side knows better,” Ri said, without elaborating.

Asked later about the remarks, Cho said there was no “special background” but attributed delays in the rail and road initiative and other cultural exchanges to “each other’s circumstances”.

The rail and road initiative and the joint Olympics bid were agreed by Moon and Kim at their latest summit, in the North Korean capital, Pyongyang.

Moon also said the North would permanently abolish key missile facilities in the presence of foreign experts.

Trump said on Wednesday South Korea would not lift sanctions on North Korea without U.S. approval.